How to use Newton-Ramphson method to find an equation root?
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Hi, I want to make all of them one M-file by making the second and the third M-file as anonymous functions in the main M-file( f and df are defined as anonymous functions).
THE CURRENT MAIN CODE
function [p0,err,k,y]=newtonlab(f,df,p0,delta,epsilon,max1)
%Input - f is the object function
% - df is the derivative of f
% - p0 is the initial approximation to a zero of f
% - delta is the tolerance for p0
% - epsilon is the tolerance for the function values y
% - max1 is the maximum number of iterations
%Output - p0 is the Newton-Raphson approximation to the zero
% - err is the error estimate for p0
% - k is the number of iterations
% - y is the function value f(p0)
%If f and df are defined as M-file functions use the @ notation
% call [p0,err,k,y]=newton(@f,@df,p0,delta,epsilon,max1).
%If f and df are defined as anonymous functions use the
% call [p0,err,k,y]=newton(f,df,p0,delta,epsilon,max1).
% NUMERICAL METHODS: Matlab Programs
for k=1:max1
p1=p0-f(p0)/df(p0);
err=abs(p1-p0);
relerr=2*err/(abs(p1)+delta);
p0=p1;
y=f(p0);
if (err<delta)|(relerr<delta)|(abs(y)<epsilon),break,end
end
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*SECOND M_FILE *_ITALIC TEXT_
function y=f(x)
%%input to function
format short e;
Params = load('saved_data.mat');
theta = pi/2;
zeta = cos(theta);
I = eye(Params.n,Params.n);
Q = zeta*I-Params.p*Params.p';
%T is a matrix(5,5)
Mroot = Params.M.^(1/2); %optimization
T = Mroot*Q*Mroot;
%find the eigen values
E =real( eig(T));
%find the negative eigen values -- %find the smallest negative eigen value
gamma = min(E);
%now solve for lambda
M_inv = inv(Params.M); %optimization
zm = Params.zm;
y= zm'*M_inv*inv(M_inv+x.*Q)*M_inv*zm;
THE THIRD M_FILE:
function y1=df(x)
%%%%input to the equation
Params = load('saved_data.mat');
theta = pi/2;
zeta = cos(theta);
I = eye(Params.n,Params.n);
Q = zeta*I-Params.p*Params.p';
%T is a matrix(5,5)
Mroot = Params.M.^(1/2); %optimization
T = Mroot*Q*Mroot;
%find the eigen values
E =real( eig(T));
%find the negative eigen values -- %find the smallest negative eigen value
gamma = min(E);
%now solve for lambda
M_inv = inv(Params.M); %optimization
zm = Params.zm;
y1=-zm'*M_inv*inv(M_inv+x.*Q)*Q*M_inv*zm;
1 Kommentar
Walter Roberson
am 1 Dez. 2011
Is this question asking something different than your previous question, http://www.mathworks.com/matlabcentral/answers/22711-newton-raphson-method ? If not then the two should be merged together and one of them deleted.
Akzeptierte Antwort
Walter Roberson
am 1 Dez. 2011
λ is not a valid variable name in MATLAB. This code would never have passed m-lint. Please do basic error checking on your code before you post it.
It is fairly unlikely that a program would use both fzero() and Newton Raphson.
[EDIT: Dec 4 2011 17:42 CDT - put in explicit merged code]
function newtonlab_driver
[p0, err, k, y] = newtonlab(@f, @df, 0, 100, 1e-8, 1000);
fprintf(1, 'Best answer was %g at lambda = %g\n', p0, y);
function [p0,err,k,y]=newtonlab(f,df,p0,delta,epsilon,max1)
%Input - f is the object function
% - df is the derivative of f
% - p0 is the initial approximation to a zero of f
% - delta is the tolerance for p0
% - epsilon is the tolerance for the function values y
% - max1 is the maximum number of iterations
%Output - p0 is the Newton-Raphson approximation to the zero
% - err is the error estimate for p0
% - k is the number of iterations
% - y is the function value f(p0)
%If f and df are defined as M-file functions use the @ notation
% call [p0,err,k,y]=newton(@f,@df,p0,delta,epsilon,max1).
%If f and df are defined as anonymous functions use the
% call [p0,err,k,y]=newton(f,df,p0,delta,epsilon,max1).
% NUMERICAL METHODS: Matlab Programs
for k=1:max1
p1=p0-f(p0)/df(p0);
err=abs(p1-p0);
relerr=2*err/(abs(p1)+delta);
p0=p1;
y=f(p0);
if (err<delta)|(relerr<delta)|(abs(y)<epsilon),break,end
end
function y=f(x)
%%input to function
format short e;
Params = load('saved_data.mat');
theta = pi/2;
zeta = cos(theta);
I = eye(Params.n,Params.n);
Q = zeta*I-Params.p*Params.p';
%T is a matrix(5,5)
Mroot = Params.M.^(1/2); %optimization
T = Mroot*Q*Mroot;
%find the eigen values
E =real( eig(T));
%find the negative eigen values -- %find the smallest negative eigen value
gamma = min(E);
%now solve for lambda
M_inv = inv(Params.M); %optimization
zm = Params.zm;
y= zm'*M_inv*inv(M_inv+x.*Q)*M_inv*zm;
function y1=df(x)
%%%%input to the equation
Params = load('saved_data.mat');
theta = pi/2;
zeta = cos(theta);
I = eye(Params.n,Params.n);
Q = zeta*I-Params.p*Params.p';
%T is a matrix(5,5)
Mroot = Params.M.^(1/2); %optimization
T = Mroot*Q*Mroot;
%find the eigen values
E =real( eig(T));
%find the negative eigen values -- %find the smallest negative eigen value
gamma = min(E);
%now solve for lambda
M_inv = inv(Params.M); %optimization
zm = Params.zm;
y1=-zm'*M_inv*inv(M_inv+x.*Q)*Q*M_inv*zm;
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