i Checked calculation and found The solution does not accord with the equation

i used the matlab to solve the nolinear equation and put the solution in and found The solution does not accord with the equation

codes are as this

function program

function F = root2d(x)
%syms equa1sub equa2sub equa3sub equa4sub equa5sub equa6sub;
equa1sub =x(1)[phone]/281474976710656+(4153907340440276559918386333329/10141204801825835211973625643008+43872868936278563423508777924017/40564819207303340847894502572032*i)*x(4)-31910460946994608903643004387955/166153499473114484112975882535043072*x(5)+35907622679629336125438914937027/340282366920938463463374607431768211456*x(6);
equa2sub =x(2)+2179336774425063/9007199254740992-(2329631036423340670360942191305/53099476611423827671670350413824+6151292551464022570539684130455/53099476611423827671670350413824*i)*x(4)+1230493617143412223713722747795/1205242255167036818169426968838144*x(5)-139908178482254182174291657953/1085297737296852063790297074655821824*x(6);
equa3sub =x(3)-2179336774425063/36028797018963968+(17783443026132371529472841155/1491110427947729683792430891008+6151292551464022570539684130455/195335466061152588576808446722048*i)*x(4)+8613455320003885565996059234565/100800544111222430647960069182849024*x(5)+7228589221583132745671735660905/18787405208694330145359816318357864448*x(6);
equa4sub =x(4)+(1160967565235845/562949953421312+5122727319147305/18014398509481984*i)*(-2659506518368929/2251799813685248-43918910449825605755648012145/51854957628343581710615576576*x(2)+17710809864611394710166972861235/18312699943233055179075791880192*x(3));
equa5sub =x(5)+7314742574589651/281474976710656+14883446107327026008787450489355/16091720173204913572666146816*x(2)+15630005759314515809316534852965/48065444999324050258617434112*x(3);
equa6sub =x(6)-8743945551921635/549755813888-40127679390402942495192578739/308460169349260713656320*x(2)+6967229325491925089773435036915/4271761374342152099725312*x(3);
 


F(1)=equa1sub;
F(2)=equa2sub;
F(3)=equa3sub;
F(4)=equa4sub;
F(5)=equa5sub;
F(6)=equa6sub;
 

main program

clc;
clear all;
close all;

fun = @root2d;
%x0 = [0,0,0,0,0,0];
x0 = [1,1,1,1,1,1];
%x =fsolve(fun,x0)

x=vpa(fsolve(fun,x0),5)';

alpha0=x(1)
alpha1 = x(2)
alpha2 =x(3)
  a0  =   x(4)
  a1 =   x(5)
  a2 =   x(6)

solutions are as this

  Optimization terminated: norm of relative change in X is less
 than max(options.TolX^2,eps) and  sum-of-squares of function 
 values is less than sqrt(options.TolFun).
 
alpha0 =
 
-3.0311-.40115*i
 
 
 
alpha1 =
 
-1.4434+.83345*i
 
 
 
alpha2 =
 
-.89752e-1+.49208e-1*i
 
 
 
a0 =
 
.28084+1.3447*i
 
 
 
a1 =
 
1338.2-786.87*i
 
 
 
a2 =
 
-25475.+28166.*i
 
 
>> 

but when i put the solution in and found The solution does not accord with the equation

why

[madhan ravi]

you mean you substituted the values back in the equation?

[dcydhb dcydhb]

yes

Answer 1

[Walter Roberson]

You have

x=vpa(fsolve(fun,x0),5)';

which takes the solution returned by fsolve, takes the complex conjugate transpose, and truncates it to 5 decimal places. The truncated complex conjugates are not good solutions.

Remember, in MATLAB ' is complex conjugate transpose, not simple transpose.

Note: your functions are linear and so could be solved using \

[dcydhb dcydhb]

but if i use vpa

i get

alpha0 =

  -3.0311 + 0.4012i

if you don't use vpa,you just get

  x =

  1.0e+004 *

  Columns 1 through 4 

  -0.0003 + 0.0000i

which has a big difference

[Walter Roberson]

The problem is the ' not the vpa . You need .' rather than '

x=vpa(fsolve(fun,x0),5).';

Answer 2

[Stephan]

Hi,

this version works fine for me:

fun = @root2d;
x0 = [1,1,1,1,1,1];
x = fsolve(fun,x0)
result = fun(x)

function F = root2d(x)
%syms equa1sub equa2sub equa3sub equa4sub equa5sub equa6sub;
F(1) =x(1)[phone]/281474976710656+(4153907340440276559918386333329/10141204801825835211973625643008+43872868936278563423508777924017/40564819207303340847894502572032*i)*x(4)-31910460946994608903643004387955/166153499473114484112975882535043072*x(5)+35907622679629336125438914937027/340282366920938463463374607431768211456*x(6);
F(2) =x(2)+2179336774425063/9007199254740992-(2329631036423340670360942191305/53099476611423827671670350413824+6151292551464022570539684130455/53099476611423827671670350413824*i)*x(4)+1230493617143412223713722747795/1205242255167036818169426968838144*x(5)-139908178482254182174291657953/1085297737296852063790297074655821824*x(6);
F(3) =x(3)-2179336774425063/36028797018963968+(17783443026132371529472841155/1491110427947729683792430891008+6151292551464022570539684130455/195335466061152588576808446722048*i)*x(4)+8613455320003885565996059234565/100800544111222430647960069182849024*x(5)+7228589221583132745671735660905/18787405208694330145359816318357864448*x(6);
F(4) =x(4)+(1160967565235845/562949953421312+5122727319147305/18014398509481984*i)*(-2659506518368929/2251799813685248-43918910449825605755648012145/51854957628343581710615576576*x(2)+17710809864611394710166972861235/18312699943233055179075791880192*x(3));
F(5) =x(5)+7314742574589651/281474976710656+14883446107327026008787450489355/16091720173204913572666146816*x(2)+15630005759314515809316534852965/48065444999324050258617434112*x(3);
F(6) =x(6)-8743945551921635/549755813888-40127679390402942495192578739/308460169349260713656320*x(2)+6967229325491925089773435036915/4271761374342152099725312*x(3);
end

result is:

Equation solved, fsolve stalled.

fsolve stopped because the relative size of the current step is less than the
default value of the step size tolerance squared and the vector of function values
is near zero as measured by the default value of the function tolerance.

<stopping criteria details>


x =

   1.0e+04 *

  -0.0003 + 0.0000i  -0.0001 - 0.0001i  -0.0000 - 0.0000i   0.0000 - 0.0001i   0.1338 + 0.0787i  -2.5475 - 2.8166i


result =

   1.0e-10 *

   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 - 0.0000i   0.0000 + 0.0000i   0.0014 - 0.0001i   0.0000 + 0.1455i

Best regards

Stephan

[dcydhb dcydhb]

so do you mean the

x = fsolve(fun,x0)
result = fun(x)

the x is the solution and the result is to put the solution in the equation?

[dcydhb dcydhb]

and also i put the solution in and the codes are as this

clc;
clear all;
close all;

alpha0 =1.0e+004 *( -0.0003 + 0.0000i );
alpha1 =1.0e+004 *(  -0.0001 - 0.0001i);
 alpha2 =1.0e+004 *(  -0.0000 - 0.0000i  );
a0 =1.0e+004 *(0.0000 - 0.0001i);
a1=1.0e+004 *(    0.1338 + 0.0787i );
a2 =1.0e+004 *(-2.5475 - 2.8166i );

x(1)=alpha0;
  x(2)=alpha1;
x(3)=alpha2 ;
   x(4)=  a0  ;
   x(5)=  a1 ;
     x(6)= a2;

x(1)[phone]/281474976710656+(4153907340440276559918386333329/10141204801825835211973625643008+43872868936278563423508777924017/40564819207303340847894502572032*i)*x(4)-31910460946994608903643004387955/166153499473114484112975882535043072*x(5)+35907622679629336125438914937027/340282366920938463463374607431768211456*x(6)
x(2)+2179336774425063/9007199254740992-(2329631036423340670360942191305/53099476611423827671670350413824+6151292551464022570539684130455/53099476611423827671670350413824*i)*x(4)+1230493617143412223713722747795/1205242255167036818169426968838144*x(5)-139908178482254182174291657953/1085297737296852063790297074655821824*x(6)
x(3)-2179336774425063/36028797018963968+(17783443026132371529472841155/1491110427947729683792430891008+6151292551464022570539684130455/195335466061152588576808446722048*i)*x(4)+8613455320003885565996059234565/100800544111222430647960069182849024*x(5)+7228589221583132745671735660905/18787405208694330145359816318357864448*x(6)
x(4)+(1160967565235845/562949953421312+5122727319147305/18014398509481984*i)*(-2659506518368929/2251799813685248-43918910449825605755648012145/51854957628343581710615576576*x(2)+17710809864611394710166972861235/18312699943233055179075791880192*x(3))
x(5)+7314742574589651/281474976710656+14883446107327026008787450489355/16091720173204913572666146816*x(2)+15630005759314515809316534852965/48065444999324050258617434112*x(3)
x(6)-8743945551921635/549755813888-40127679390402942495192578739/308460169349260713656320*x(2)+6967229325491925089773435036915/4271761374342152099725312*x(3)

the result

ans =

  -0.4567 - 0.5637i


ans =

   0.4954 - 0.1490i


ans =

   0.0755 + 0.0445i


ans =

  -0.9299 + 0.6517i


ans =

  4.3907e+002 -1.3791e+002i


ans =

  8.8710e+004 +1.0192e+005i

>> 

they are not 0

[Walter Roberson]

Before you display the values in x, give the command

format long g

Now display x again. You will find some of them are quite different from what you copied.

[dcydhb dcydhb]

thanks a lot,it works well,

but why it has a big difference when i use

alpha0 =-3.0311-.40115*i;
alpha1 =-1.4434+.83345*i;
 alpha2 =-.89752e-1+.49208e-1*i;
a0 =.28084+1.3447*i;
a1 =1338.2-786.87*i;
a2 =-25475.+28166.*i;

i get

ans =

          -2.90871132396907 +     0.607484578051479i


ans =

          0.311531099632365 -    0.0650666606923589i


ans =

        -0.0846890466989907 +    0.0176878639974451i


ans =

          0.374490074032625 -    0.0258183590976351i


ans =

        -0.0183929950145583 +   0.00053882521234172i


ans =

           6.98186657158658 +     0.322983928941539i

>> 

and when i use your format long,use

alpha0 = -3.0311134536181 +     0.401152454231559i;
alpha1 = -1.44335136284869 -     0.833446193001501i;
 alpha2 = -0.0897522685127253 -    0.0492077544975424i;
a0 =0.280837251730613 -      1.34470093706138i;
a1=1338.17349516203 +      786.866937848724i;
a2 =  -25475.2167010186 -      28165.5821761859i;

i get

ans =

      7.16657636012918e-015 - 9.82720849140861e-016i


ans =

     -3.83026943495679e-015 + 2.64979010955457e-016i


ans =

      1.43982048506075e-016 - 4.85722573273506e-017i


ans =

      7.43849426498855e-015 - 3.10862446895044e-015i


ans =

     -3.29336558024806e-012 - 8.88178419700125e-014i


ans =

      4.94765117764473e-010 - 4.36557456851006e-011i

>> 

[Walter Roberson]

You took the complex conjugate at some point by using ' instead of .'

[dcydhb dcydhb]

i mean if i don't use the format long,i get the answer

alpha0 =-3.0311-.40115*i;
alpha1 =-1.4434+.83345*i;
 alpha2 =-.89752e-1+.49208e-1*i;
a0 =.28084+1.3447*i;
a1 =1338.2-786.87*i;
a2 =-25475.+28166.*i;

if i use format long,i get

alpha0 = -3.0311134536181 +     0.401152454231559i;
alpha1 = -1.44335136284869 -     0.833446193001501i;
 alpha2 = -0.0897522685127253 -    0.0492077544975424i;
a0 =0.280837251730613 -      1.34470093706138i;
a1=1338.17349516203 +      786.866937848724i;
a2 =  -25475.2167010186 -      28165.5821761859i;

and when i put the soution in the equation,the former has the Precision

such as

ans =
           6.98186657158658 +     0.322983928941539i

while the latter has the Precision such as

           ans =
      4.94765117764473e-010 - 4.36557456851006e-011i

why has a big difference

[Walter Roberson]

Please post your current code.

[dcydhb dcydhb]

codes are as this

using format long ,i get the answer

alpha0 = -3.0311134536181 +     0.401152454231559i;
alpha1 = -1.44335136284869 -     0.833446193001501i;
 alpha2 = -0.0897522685127253 -    0.0492077544975424i;
a0 =0.280837251730613 -      1.34470093706138i;
a1=1338.17349516203 +      786.866937848724i;
a2 =  -25475.2167010186 -      28165.5821761859i;

and put it in the program

clc;
clear all;
close all;


alpha0 =-0.902612530938861 +      2.16356827387381i;
alpha1 = -0.18816334103255 -     0.122205949485723i;
alpha2 =  0.0572191359187823 +     0.040682702643867i;
a0 =  2.03364667845748 -    0.0196408376693919i;
a1 = 129.438386669641 +      99.7957252883904i;
a2 =   -101899.136979033 -      82252.7316082889i;




x(1)=alpha0;
  x(2)=alpha1;
x(3)=alpha2 ;
   x(4)=  a0  ;
   x(5)=  a1 ;
     x(6)= a2;

equa1sub =x(1)[phone]/281474976710656-(4154756651791824122955846205623/10141204801825835211973625643008+10968068365840776354319913193387/10141204801825835211973625643008*i)*x(4)+15954949269969134648023144147861/83076749736557242056487941267521536*x(5)-71813660819499486824121496911249/680564733841876926926749214863536422912*x(6)
 
equa2sub =x(2)+2179336774425063/9007199254740992+(37526423397676813332334898889027/855220629711474430592113990172672+49532669641878859065350990413901/427610314855737215296056995086336*i)*x(4)-7398539084151252801240731883817/7245856949184205584664105964273664*x(5)+9701869628173919811376223237191/75261204389257980309851363976180400128*x(6)
  
equa3sub =x(3)-2179336774425063/36028797018963968-(12508807799225604444111632963009/1048697196988140797536670555570176+49532669641878859065350990413901/1573045795482211196305005833355264*i)*x(4)-7398539084151252801240731883817/86588217623736540910447134758666240*x(5)-29105608884521759434128669711573/75649093851100752735482115538246696960*x(6)
 
equa4sub =x(4)+(2322028850419079/1125899906842624+2562706364895407/9007199254740992*i)*(-5318998413755481/4503599627370496-2829251784246184997786270102985/3340705584810446994500445274112*x(2)+1485584096701532954999143830883/1536177534650596871391607259136*x(3))
  
equa5sub =x(5)+1828304033752709/70368744177664+798857101094098914621327367885/863773459098840425570500608*x(2)+3355712380299671672017873907067/10322119906394069303327457280*x(3)
 
equa6sub =x(6)-8744181223955479/549755813888-8904871213428984377698427416207/68449666641079584505724928*x(2)+56109258842949034654051535392393/34401225025749569220116480*x(3)
 

i get

equa1sub =

  4.7011e-016 +3.7643e-015i


equa2sub =

 -1.0582e-016 +3.4694e-017i


equa3sub =

  2.2898e-016 -2.0817e-017i


equa4sub =

 -4.4409e-016 -2.8103e-016i


equa5sub =

 -6.7146e-013 +1.1191e-013i


equa6sub =

 -2.4738e-010 -7.2760e-011i

>> 

while when don't use format long

i get the answer

alpha0 =-3.0311-.40115*i;
alpha1 =-1.4434+.83345*i;
 alpha2 =-.89752e-1+.49208e-1*i;
a0 =.28084+1.3447*i;
a1 =1338.2-786.87*i;
a2 =-25475.+28166.*i;

and put it in the program

clc;
clear all;
close all;


alpha0 =-3.0311-.40115*i;
alpha1 =-1.4434+.83345*i;
 alpha2 =-.89752e-1+.49208e-1*i;
a0 =.28084+1.3447*i;
a1 =1338.2-786.87*i;
a2 =-25475.+28166.*i;




x(1)=alpha0;
  x(2)=alpha1;
x(3)=alpha2 ;
   x(4)=  a0  ;
   x(5)=  a1 ;
     x(6)= a2;

equa1sub =x(1)[phone]/281474976710656-(4154756651791824122955846205623/10141204801825835211973625643008+10968068365840776354319913193387/10141204801825835211973625643008*i)*x(4)+15954949269969134648023144147861/83076749736557242056487941267521536*x(5)-71813660819499486824121496911249/680564733841876926926749214863536422912*x(6)
 
equa2sub =x(2)+2179336774425063/9007199254740992+(37526423397676813332334898889027/855220629711474430592113990172672+49532669641878859065350990413901/427610314855737215296056995086336*i)*x(4)-7398539084151252801240731883817/7245856949184205584664105964273664*x(5)+9701869628173919811376223237191/75261204389257980309851363976180400128*x(6)
  
equa3sub =x(3)-2179336774425063/36028797018963968-(12508807799225604444111632963009/1048697196988140797536670555570176+49532669641878859065350990413901/1573045795482211196305005833355264*i)*x(4)-7398539084151252801240731883817/86588217623736540910447134758666240*x(5)-29105608884521759434128669711573/75649093851100752735482115538246696960*x(6)
 
equa4sub =x(4)+(2322028850419079/1125899906842624+2562706364895407/9007199254740992*i)*(-5318998413755481/4503599627370496-2829251784246184997786270102985/3340705584810446994500445274112*x(2)+1485584096701532954999143830883/1536177534650596871391607259136*x(3))
  
equa5sub =x(5)+1828304033752709/70368744177664+798857101094098914621327367885/863773459098840425570500608*x(2)+3355712380299671672017873907067/10322119906394069303327457280*x(3)
 
equa6sub =x(6)-8744181223955479/549755813888-8904871213428984377698427416207/68449666641079584505724928*x(2)+56109258842949034654051535392393/34401225025749569220116480*x(3)
 

and i get

equa1sub =

   0.2893 - 1.4099i


equa2sub =

  -2.7146 + 1.7321i


equa3sub =

  -0.2158 + 0.0807i


equa4sub =

   0.3744 - 0.0258i


equa5sub =

   0.0813 - 0.0599i


equa6sub =

   8.9329 - 1.1249i

>> 

which has a big difference comparing with the format long

[Walter Roberson]

Are you still using your posted main program,

clc;
clear all;
close all;
fun = @root2d;
%x0 = [0,0,0,0,0,0];
x0 = [1,1,1,1,1,1];
%x =fsolve(fun,x0)
x=vpa(fsolve(fun,x0),5)';
alpha0=x(1)
alpha1 = x(2)
alpha2 =x(3)
  a0  =   x(4)
  a1 =   x(5)
  a2 =   x(6)

If so then you need to correct the line

  x=vpa(fsolve(fun,x0),5)';

to

  x=vpa(fsolve(fun,x0),5).';

[dcydhb dcydhb]

so do you mean it is not the precision but the Conjugate?

  x=vpa(fsolve(fun,x0),5).';

your method really solve the problem but why using vpa,it appears the Conjugate problem?

[Walter Roberson]

The vpa() gives some inaccuracy, but it is the complex conjugate that was really messing things up for you.

[dcydhb dcydhb]

thanks a lot,the question ahs been solevd but another question appears,

when i increase the Expansion item number，form 6 equations to 12 equations,

codes are as this

function codes

function F = root2d(x)
%syms equa1sub equa2sub equa3sub equa4sub equa5sub equa6sub;
equa1sub =x(1)[phone]/281474976710656-(4154756651791824122955846205623/10141204801825835211973625643008+10968068365840776354319913193387/10141204801825835211973625643008*i)*x(7)+15954949269969134648023144147861/83076749736557242056487941267521536*x(8)-71813660819499486824121496911249/680564733841876926926749214863536422912*x(9)+68704458373558018815486967994675/1393796574908163946345982392040522594123776*x(10)-26218118780833903306440628355937/1427247692705959881058285969449495136382746624*x(11)+206796938269122258779026599337/91343852333181432387730302044767688728495783936*x(12);
 
equa2sub =x(2)+2179336774425063/9007199254740992+(37526423397676813332334898889027/855220629711474430592113990172672+49532669641878859065350990413901/427610314855737215296056995086336*i)*x(7)-7398539084151252801240731883817/7245856949184205584664105964273664*x(8)+9701869628173919811376223237191/75261204389257980309851363976180400128*x(9)-1277211448906621552448654388595/23860751773952951312363398400278311993344*x(10)+1362802704850279953288683880255/70907773931469299065694310054832901202116608*x(11)-8625402993825599933615303699537/3702438626946186324992873082646789575845217304576*x(12);
 
equa3sub =x(3)-2179336774425063/36028797018963968-(12508807799225604444111632963009/1048697196988140797536670555570176+49532669641878859065350990413901/1573045795482211196305005833355264*i)*x(7)-7398539084151252801240731883817/86588217623736540910447134758666240*x(8)-29105608884521759434128669711573/75649093851100752735482115538246696960*x(9)+1277211448906621552448654388595/17711241862742021199068701875804540239872*x(10)-1362802704850279953288683880255/61068558073531812431847844722400210020466688*x(11)+8625402993825599933615303699537/3380027201713290762974992106633635151204912726016*x(12);

equa4sub =x(4)+7748752975733557/288230376151711744+(33356820797934943209001720132433/6190408764194964734552061289431040+22014519840835049131921318329153/1547602191048741183638015322357760*i)*x(7)+26305916743648898510433925203569/863922993464667543602663285577482240*x(8)-51743304683594236328831377155201/310355742240037684763822436037613846528*x(9)-36329570102232795753818397281155/212254113490217598493003436507731431784448*x(10)+19382082913426203433050528326643/635304746339119300790994312862157102563459072*x(11)-2555674961133510611575096049613/842274022614853767674660051874414976259181248512*x(12);

equa5sub =x(5)-2179336774425063/144115188075855872-(37526423397676813332334898889027/12309575435976212511299345462591488+49532669641878859065350990413901/6154787717988106255649672731295744*i)*x(7)-7398539084151252801240731883817/461924515915419508444148023940874240*x(8)+29105608884521759434128669711573/524888983415592000040805790022931316736*x(9)-1277211448906621552448654388595/6886797782101713761219919597640643248128*x(10)-151422522761142217032075986695/2412410515753537353989004504838094190542848*x(11)+8625402993825599933615303699537/2090381500781707541347807227300837103175632683008*x(12);
 
equa6sub =x(6)+5579102142528161/576460752303423488+(37526423397676813332334898889027/19182188319735057694389731174907904+49532669641878859065350990413901/9591094159867528847194865587453952*i)*x(7)+7398539084151252801240731883817/743426739634181641860703322279772160*x(8)-29105608884521759434128669711573/975292541365611677959817308065299955712*x(9)+1277211448906621552448654388595/25335327515734513772510566088095356157952*x(10)-454267568283426651096227960085/2601984310676884475399766100960607803015168*x(11)-8625402993825599933615303699537/1123147225083019881738503323981193479786657218560*x(12);

equa7sub =x(7)+(2322028850419079/1125899906842624+2562706364895407/9007199254740992*i)*(-5318998413755481/4503599627370496-11316947028382809420225314005533/13362822339241787978001781096448*x(2)+47539893266487660052480027409623/49157681108819099884531432292352*x(3)-9653174320626376094416784221761/9672513694054632397737595764736*x(4)+48624853531325315583340957398461/48084279046782080122263068213248*x(5)-19076967537554081507840067761767/18732605780991267279677471850496*x(6));
 
equa8sub =x(8)+1828304033752709/70368744177664+12781645729332806833062081373649/13820375345581446809128009728*x(2)+41947465506445508270841202315/129026498829925866291593216*x(3)-106470105689011260713633181571/402295493271512698197114880*x(4)+143015982726173118919053113709/573600972587142771040583680*x(5)-21546008834667373653917509482703/88623373464844422562206187520*x(6);
 
equa9sub =x(9)-8744181223955479/549755813888-53428943499171695984835881591627/410697999846477507034349568*x(2)+56110677749960030092146867614297/34401225025749569220116480*x(3)+28483769964134474313932345620805/17641681452007428831838208*x(4)-14347810331846682779060483651413/14918242169858103808360448*x(5)+22516280630792217615492161016547/27719481220333695943049216*x(6);
 
equa10sub =x(10)+2143354288027763/268435456+76889959165422172751349313276095/1324537800215405753532416*x(2)-40374630662549725282540084069465/122896428192007114981376*x(3)+40991188782415858629190320752825/23012637096507873427456*x(4)+13765354859219285845701862029855/3982229928972283543552*x(5)-64806667879765933354102588502575/43949787413105820565504*x(6);
 
equa11sub =x(11)-1743625504902557/524288-683191558149789503090357463411/29326767937702191104*x(2)+22959445633915007586210679339785/202058909099976753152*x(3)-11655028849494739207651118904051/32844485577164910592*x(4)+652317456398320801335468445423/498874802037594112*x(5)+383885133922523724333435256089/67259717998721024*x(6);
 
equa12sub =x(12)+3878949580580463/8192+19055803659565858140764297628659/5841418173556017152*x(2)-10006131399781328118029811914599/666592829503797504*x(3)+20317868644705667433246067365239/498327785943072384*x(4)-5117246172621763207417567132397/51531882592622344*x(5)+16061175637909210839969990512723/55375433542216160*x(6);
 

F(1)=equa1sub;
F(2)=equa2sub;
F(3)=equa3sub;
F(4)=equa4sub;
F(5)=equa5sub;
F(6)=equa6sub;

F(7)=equa7sub;
F(8)=equa8sub;
F(9)=equa9sub;
F(10)=equa10sub;
F(11)=equa11sub;
F(12)=equa12sub;
 

main program codes

clc;
clear all;
close all;


fun = @root2d;
x0 = [1,1,1,1,1,1,1,1,1,1,1,1];
format long g
x = fsolve(fun,x0);
result = fun(x);



alpha0=x(1)
alpha1 = x(2)
alpha2 =x(3)
alpha3=x(4)
alpha4 = x(5)
alpha5 =x(6)

  a0  =   x(7)
  a1 =   x(8)
  a2 =   x(9)
    a3  =   x(10)
  a4 =   x(11)
  a5 =   x(12)
  

i get 12 roots,but when i put the answers in and the answer doesn't satisify the equation and why?

i didn't use the vpa

and the hints are as this

  Maximum number of function evaluations reached:
 increase options.MaxFunEvals.

[dcydhb dcydhb]

so how to set the options

such as this?

options= struct('MaxFunEvals',10000,'MaxIter', 10000);

x = fsolve(fun,x0,options);

[Walter Roberson]

You have the Symbolic Toolbox, use it.

X = sym('x', [1 12]);
[A, b] = equationsToMatrix(root2d(X));
x = A\b;
xd = double(x);

Note that your matrix is singular to within double precision:

rank(double(A))        % -> 6
rank(A)                % -> 12

This is because you add some relatively small values.

Your code is misleading you about how much precision is available. You have obviously converted it from symbolic code without taking into account that numeric code does not have that much precision. You should go back to symbolic code:

function F = root2d(x)
    S = @(v) sym(v);
    equa1sub =x(1)+S('484533722967603')/S('281474976710656')-S('4154756651791824122955846205623')/S('10141204801825835211973625643008')+S('10968068365840776354319913193387')/S('10141204801825835211973625643008')*1i*x(7)+S('15954949269969134648023144147861')/S('83076749736557242056487941267521536')*x(8)-S('71813660819499486824121496911249')/S('680564733841876926926749214863536422912')*x(9)+S('68704458373558018815486967994675')/S('1393796574908163946345982392040522594123776')*x(10)-S('26218118780833903306440628355937')/S('1427247692705959881058285969449495136382746624')*x(11)+S('206796938269122258779026599337')/S('91343852333181432387730302044767688728495783936')*x(12);
    
    equa2sub =x(2)+S('2179336774425063')/S('9007199254740992')+S('37526423397676813332334898889027')/S('855220629711474430592113990172672')+S('49532669641878859065350990413901')/S('427610314855737215296056995086336')*1i*x(7)-S('7398539084151252801240731883817')/S('7245856949184205584664105964273664')*x(8)+S('9701869628173919811376223237191')/S('75261204389257980309851363976180400128')*x(9)-S('1277211448906621552448654388595')/S('23860751773952951312363398400278311993344')*x(10)+S('1362802704850279953288683880255')/S('70907773931469299065694310054832901202116608')*x(11)-S('8625402993825599933615303699537')/S('3702438626946186324992873082646789575845217304576')*x(12);
    
    equa3sub =x(3)-S('2179336774425063')/S('36028797018963968')-S('12508807799225604444111632963009')/S('1048697196988140797536670555570176')+S('49532669641878859065350990413901')/S('1573045795482211196305005833355264')*1i*x(7)-S('7398539084151252801240731883817')/S('86588217623736540910447134758666240')*x(8)-S('29105608884521759434128669711573')/S('75649093851100752735482115538246696960')*x(9)+S('1277211448906621552448654388595')/S('17711241862742021199068701875804540239872')*x(10)-S('1362802704850279953288683880255')/S('61068558073531812431847844722400210020466688')*x(11)+S('8625402993825599933615303699537')/S('3380027201713290762974992106633635151204912726016')*x(12);
    equa4sub =x(4)+S('7748752975733557')/S('288230376151711744')+S('33356820797934943209001720132433')/S('6190408764194964734552061289431040')+S('22014519840835049131921318329153')/S('1547602191048741183638015322357760')*1i*x(7)+S('26305916743648898510433925203569')/S('863922993464667543602663285577482240')*x(8)-S('51743304683594236328831377155201')/S('310355742240037684763822436037613846528')*x(9)-S('36329570102232795753818397281155')/S('212254113490217598493003436507731431784448')*x(10)+S('19382082913426203433050528326643')/S('635304746339119300790994312862157102563459072')*x(11)-S('2555674961133510611575096049613')/S('842274022614853767674660051874414976259181248512')*x(12);
    equa5sub =x(5)-S('2179336774425063')/S('144115188075855872')-S('37526423397676813332334898889027')/S('12309575435976212511299345462591488')+S('49532669641878859065350990413901')/S('6154787717988106255649672731295744')*1i*x(7)-S('7398539084151252801240731883817')/S('461924515915419508444148023940874240')*x(8)+S('29105608884521759434128669711573')/S('524888983415592000040805790022931316736')*x(9)-S('1277211448906621552448654388595')/S('6886797782101713761219919597640643248128')*x(10)-S('151422522761142217032075986695')/S('2412410515753537353989004504838094190542848')*x(11)+S('8625402993825599933615303699537')/S('2090381500781707541347807227300837103175632683008')*x(12);
    
    equa6sub =x(6)+S('5579102142528161')/S('576460752303423488')+S('37526423397676813332334898889027')/S('19182188319735057694389731174907904')+S('49532669641878859065350990413901')/S('9591094159867528847194865587453952')*1i*x(7)+S('7398539084151252801240731883817')/S('743426739634181641860703322279772160')*x(8)-S('29105608884521759434128669711573')/S('975292541365611677959817308065299955712')*x(9)+S('1277211448906621552448654388595')/S('25335327515734513772510566088095356157952')*x(10)-S('454267568283426651096227960085')/S('2601984310676884475399766100960607803015168')*x(11)-S('8625402993825599933615303699537')/S('1123147225083019881738503323981193479786657218560')*x(12);
    equa7sub =x(7)+S('2322028850419079')/S('1125899906842624')+S('2562706364895407')/S('9007199254740992')*1i-S('5318998413755481')/S('4503599627370496')-S('11316947028382809420225314005533')/S('13362822339241787978001781096448')*x(2)+S('47539893266487660052480027409623')/S('49157681108819099884531432292352')*x(3)-S('9653174320626376094416784221761')/S('9672513694054632397737595764736')*x(4)+S('48624853531325315583340957398461')/S('48084279046782080122263068213248')*x(5)-S('19076967537554081507840067761767')/S('18732605780991267279677471850496')*x(6);
    
    equa8sub =x(8)+S('1828304033752709')/S('70368744177664')+S('12781645729332806833062081373649')/S('13820375345581446809128009728')*x(2)+S('41947465506445508270841202315')/S('129026498829925866291593216')*x(3)-S('106470105689011260713633181571')/S('402295493271512698197114880')*x(4)+S('143015982726173118919053113709')/S('573600972587142771040583680')*x(5)-S('21546008834667373653917509482703')/S('88623373464844422562206187520')*x(6);
    
    equa9sub =x(9)-S('8744181223955479')/S('549755813888')-S('53428943499171695984835881591627')/S('410697999846477507034349568')*x(2)+S('56110677749960030092146867614297')/S('34401225025749569220116480')*x(3)+S('28483769964134474313932345620805')/S('17641681452007428831838208')*x(4)-S('14347810331846682779060483651413')/S('14918242169858103808360448')*x(5)+S('22516280630792217615492161016547')/S('27719481220333695943049216')*x(6);
    
    equa10sub =x(10)+S('2143354288027763')/S('268435456')+S('76889959165422172751349313276095')/S('1324537800215405753532416')*x(2)-S('40374630662549725282540084069465')/S('122896428192007114981376')*x(3)+S('40991188782415858629190320752825')/S('23012637096507873427456')*x(4)+S('13765354859219285845701862029855')/S('3982229928972283543552')*x(5)-S('64806667879765933354102588502575')/S('43949787413105820565504')*x(6);
    
    equa11sub =x(11)-S('1743625504902557')/S('524288')-S('683191558149789503090357463411')/S('29326767937702191104')*x(2)+S('22959445633915007586210679339785')/S('202058909099976753152')*x(3)-S('11655028849494739207651118904051')/S('32844485577164910592')*x(4)+S('652317456398320801335468445423')/S('498874802037594112')*x(5)+S('383885133922523724333435256089')/S('67259717998721024')*x(6);
    
    equa12sub =x(12)+S('3878949580580463')/S('8192')+S('19055803659565858140764297628659')/S('5841418173556017152')*x(2)-S('10006131399781328118029811914599')/S('666592829503797504')*x(3)+S('20317868644705667433246067365239')/S('498327785943072384')*x(4)-S('5117246172621763207417567132397')/S('51531882592622344')*x(5)+S('16061175637909210839969990512723')/S('55375433542216160')*x(6);
    
    F(1)=equa1sub;
    F(2)=equa2sub;
    F(3)=equa3sub;
    F(4)=equa4sub;
    F(5)=equa5sub;
    F(6)=equa6sub;
    F(7)=equa7sub;
    F(8)=equa8sub;
    F(9)=equa9sub;
    F(10)=equa10sub;
    F(11)=equa11sub;
    F(12)=equa12sub;

You will still have the problem that rank(double(A)) is only 6, but the code I post here with equationsToMatrix will work fine with it.

[dcydhb dcydhb]

are you really sure this will work?

i get the hints

??? Error using ==> error
Formatted arguments cannot be non-scalar numeric matrices.

Error in ==> sym.sym at 100
         error('symbolic:sym:sym:errmsg4','Second argument %s not recognized.',a);

Error in ==> Untitled2 at 5
X = sym('x', [1 12]);

[dcydhb dcydhb]

and also i think it is not a convenient way to use for example you have to edit a lot in the function programs such as this,yu have to change the function program to this form

equa1sub =x(1)+S('484533722967603')/S('281474976710656')-S('4154756651791824122955846205623')/S('10141204801825835211973625643008')+S('10968068365840776354319913193387')/S('10141204801825835211973625643008')*1i*x(7)+S('15954949269969134648023144147861')/S('83076749736557242056487941267521536')*x(8)-S('71813660819499486824121496911249')/S('680564733841876926926749214863536422912')*x(9)+S('68704458373558018815486967994675')/S('1393796574908163946345982392040522594123776')*x(10)-S('26218118780833903306440628355937')/S('1427247692705959881058285969449495136382746624')*x(11)+S('206796938269122258779026599337')/S('91343852333181432387730302044767688728495783936')*x(12);
    

[Walter Roberson]

are you really sure this will work?

That syntax has been supported since R2010b. I see that you are using R2007a, which was still based on Maple rather than the MuPAD that has been used since R2008a+ and later. You will probably need to do something like:

for K = 1 : 12
    X(K) = sym( sprintf('x%d', K) );
end

i think it is not a convenient way to use

It is obvious that you are generating expressions such as x(1)[phone]/281474976710656 instead of coding them by hand. Change how you generate them, keeping in mind that for the range of values you are using, you are suffering badly from round-off error.

It looks to me as if you have very likely attempted to use floating point mixed with symbolic variables when you generated those expressions. For example you might have something like

G = 338.7;
H = 28399.4;
solve( an expression in G/H*x )

and are expecting to get sensible answers out of it.

However, it is a almost always a categorical error to use floating point constants together with solve() or any symbolic operation. What does G = 338.7 mean ? Does it mean exactly 3387/10 ? Does it mean "some number between 338.65 inclusive and 338.75 exclusive that got rounded to 338.7" ?

If you have a floating point constant that has a precise definition such as 1.8 in temperature conversion being defined as being exactly 9/5, then use sym(9)/sym(5) rather than 1.8 . And be consistent about it. For example, 1.8*1.414*x is not the same as sym(1.8)*sym(1.414) which is not the same as sym(9)/sym(5) * sqrt(sym(2))

If you have floating point numbers such as 1.602E-19 that are approximations rather than exact definitions, then you should not be using solve() with them -- not unless you are deliberately coding to take into account interval arithmetic based upon the known uncertainties in the numbers.

Remember that solve() is for finding indefinitely precise solutions according to theory. It is a mistake to ask for an indefinitely precise solution based upon formula numbers that are not themselves indefinitely precise.

[dcydhb dcydhb]

you have mentioned a way

X = sym('x', [1 12]);
[A, b] = equationsToMatrix(root2d(X));
x = A\b;
xd = double(x);

to solve the equation,and i got the answers and put them in to the equation and they are still not the root of the equation

12 equations are as this ,maybe you could try to solve it,thanks a lot

function F = root2d(x)
%syms equa1sub equa2sub equa3sub equa4sub equa5sub equa6sub;
equa1sub =x(1)[phone]/281474976710656-(4154756651791824122955846205623/10141204801825835211973625643008+10968068365840776354319913193387/10141204801825835211973625643008*i)*x(7)+15954949269969134648023144147861/83076749736557242056487941267521536*x(8)-71813660819499486824121496911249/680564733841876926926749214863536422912*x(9)+68704458373558018815486967994675/1393796574908163946345982392040522594123776*x(10)-26218118780833903306440628355937/1427247692705959881058285969449495136382746624*x(11)+206796938269122258779026599337/91343852333181432387730302044767688728495783936*x(12);
 
equa2sub =x(2)+2179336774425063/9007199254740992+(37526423397676813332334898889027/855220629711474430592113990172672+49532669641878859065350990413901/427610314855737215296056995086336*i)*x(7)-7398539084151252801240731883817/7245856949184205584664105964273664*x(8)+9701869628173919811376223237191/75261204389257980309851363976180400128*x(9)-1277211448906621552448654388595/23860751773952951312363398400278311993344*x(10)+1362802704850279953288683880255/70907773931469299065694310054832901202116608*x(11)-8625402993825599933615303699537/3702438626946186324992873082646789575845217304576*x(12);
 
equa3sub =x(3)-2179336774425063/36028797018963968-(12508807799225604444111632963009/1048697196988140797536670555570176+49532669641878859065350990413901/1573045795482211196305005833355264*i)*x(7)-7398539084151252801240731883817/86588217623736540910447134758666240*x(8)-29105608884521759434128669711573/75649093851100752735482115538246696960*x(9)+1277211448906621552448654388595/17711241862742021199068701875804540239872*x(10)-1362802704850279953288683880255/61068558073531812431847844722400210020466688*x(11)+8625402993825599933615303699537/3380027201713290762974992106633635151204912726016*x(12);

equa4sub =x(4)+7748752975733557/288230376151711744+(33356820797934943209001720132433/6190408764194964734552061289431040+22014519840835049131921318329153/1547602191048741183638015322357760*i)*x(7)+26305916743648898510433925203569/863922993464667543602663285577482240*x(8)-51743304683594236328831377155201/310355742240037684763822436037613846528*x(9)-36329570102232795753818397281155/212254113490217598493003436507731431784448*x(10)+19382082913426203433050528326643/635304746339119300790994312862157102563459072*x(11)-2555674961133510611575096049613/842274022614853767674660051874414976259181248512*x(12);

equa5sub =x(5)-2179336774425063/144115188075855872-(37526423397676813332334898889027/12309575435976212511299345462591488+49532669641878859065350990413901/6154787717988106255649672731295744*i)*x(7)-7398539084151252801240731883817/461924515915419508444148023940874240*x(8)+29105608884521759434128669711573/524888983415592000040805790022931316736*x(9)-1277211448906621552448654388595/6886797782101713761219919597640643248128*x(10)-151422522761142217032075986695/2412410515753537353989004504838094190542848*x(11)+8625402993825599933615303699537/2090381500781707541347807227300837103175632683008*x(12);
 
equa6sub =x(6)+5579102142528161/576460752303423488+(37526423397676813332334898889027/19182188319735057694389731174907904+49532669641878859065350990413901/9591094159867528847194865587453952*i)*x(7)+7398539084151252801240731883817/743426739634181641860703322279772160*x(8)-29105608884521759434128669711573/975292541365611677959817308065299955712*x(9)+1277211448906621552448654388595/25335327515734513772510566088095356157952*x(10)-454267568283426651096227960085/2601984310676884475399766100960607803015168*x(11)-8625402993825599933615303699537/1123147225083019881738503323981193479786657218560*x(12);

equa7sub =x(7)+(2322028850419079/1125899906842624+2562706364895407/9007199254740992*i)*(-5318998413755481/4503599627370496-11316947028382809420225314005533/13362822339241787978001781096448*x(2)+47539893266487660052480027409623/49157681108819099884531432292352*x(3)-9653174320626376094416784221761/9672513694054632397737595764736*x(4)+48624853531325315583340957398461/48084279046782080122263068213248*x(5)-19076967537554081507840067761767/18732605780991267279677471850496*x(6));
 
equa8sub =x(8)+1828304033752709/70368744177664+12781645729332806833062081373649/13820375345581446809128009728*x(2)+41947465506445508270841202315/129026498829925866291593216*x(3)-106470105689011260713633181571/402295493271512698197114880*x(4)+143015982726173118919053113709/573600972587142771040583680*x(5)-21546008834667373653917509482703/88623373464844422562206187520*x(6);
 
equa9sub =x(9)-8744181223955479/549755813888-53428943499171695984835881591627/410697999846477507034349568*x(2)+56110677749960030092146867614297/34401225025749569220116480*x(3)+28483769964134474313932345620805/17641681452007428831838208*x(4)-14347810331846682779060483651413/14918242169858103808360448*x(5)+22516280630792217615492161016547/27719481220333695943049216*x(6);
 
equa10sub =x(10)+2143354288027763/268435456+76889959165422172751349313276095/1324537800215405753532416*x(2)-40374630662549725282540084069465/122896428192007114981376*x(3)+40991188782415858629190320752825/23012637096507873427456*x(4)+13765354859219285845701862029855/3982229928972283543552*x(5)-64806667879765933354102588502575/43949787413105820565504*x(6);
 
equa11sub =x(11)-1743625504902557/524288-683191558149789503090357463411/29326767937702191104*x(2)+22959445633915007586210679339785/202058909099976753152*x(3)-11655028849494739207651118904051/32844485577164910592*x(4)+652317456398320801335468445423/498874802037594112*x(5)+383885133922523724333435256089/67259717998721024*x(6);
 
equa12sub =x(12)+3878949580580463/8192+19055803659565858140764297628659/5841418173556017152*x(2)-10006131399781328118029811914599/666592829503797504*x(3)+20317868644705667433246067365239/498327785943072384*x(4)-5117246172621763207417567132397/51531882592622344*x(5)+16061175637909210839969990512723/55375433542216160*x(6);
 





F(1)=equa1sub;
F(2)=equa2sub;
F(3)=equa3sub;
F(4)=equa4sub;
F(5)=equa5sub;
F(6)=equa6sub;

F(7)=equa7sub;
F(8)=equa8sub;
F(9)=equa9sub;
F(10)=equa10sub;
F(11)=equa11sub;
F(12)=equa12sub;
 

[Walter Roberson]

[A, b] = equationsToMatrix(root2d(X), X);

[dcydhb dcydhb]

i have used this

for K = 1 : 12
    X(K) = sym( sprintf('x%d', K) );
end
[A, b] = equationsToMatrix(root2d(X), X);

%[A, b] = equationsToMatrix(root2d(X));
x = A\b;
xd = double(x);


conj(vpa(x,10))

it has the best result but still has some difference,put the root in the equation i got some are still not zero

equa1sub =

   0.8957 - 0.0963i


equa2sub =

  -0.1504 - 0.2645i


equa3sub =

   0.0261 - 0.0028i


equa4sub =

  -0.0185 - 0.0325i


equa5sub =

   0.0067 - 0.0007i


equa6sub =

  -0.0067 - 0.0118i


equa7sub =

  -3.0071 + 0.0878i


equa8sub =

 -1.0658e-014 -3.2196e-015i


equa9sub =

 -3.0923e-011 +4.0927e-012i


equa10sub =

     0


equa11sub =

     0


equa12sub =

  9.7656e-004 -1.2207e-004i

>> 

[Walter Roberson]

why are you taking conj(x) ?

[dcydhb dcydhb]

without conj(x) there is more difference,and still i need the effective way to get the root of the 12 equations

[dcydhb dcydhb]

this time i use this

for K = 1 : 12
    X(K) = sym( sprintf('x%d', K) );
end
[A, b] = equationsToMatrix(root2d(X), X);

%[A, b] = equationsToMatrix(root2d(X));
x = A\b;
xd = double(x);

vpa(x,10)

i put the root in the equation and get

equa1sub =

   0.3873 + 2.6626i


equa2sub =

  -0.0959 - 0.0103i


equa3sub =

   0.0113 + 0.0775i


equa4sub =

  -0.0118 - 0.0013i


equa5sub =

   0.0029 + 0.0198i


equa6sub =

  -0.0043 - 0.0005i


equa7sub =

  -2.9789 - 0.5863i


equa8sub =

 -5.7895e-008 -8.8981e-009i


equa9sub =

  6.1587e-006 -8.7048e-006i


equa10sub =

   0.0054 + 0.0038i


equa11sub =

  38.2471 + 0.8511i


equa12sub =

  1.4872e+003 +2.0583e+002i

>> 

they are not zero so is the way effiective to solve the equation?