Using fsolve inside an other fsolve

Hi everyone,

How can I use the result of each iteration fsolve as the initial guess for other fsolve. My code is like that: The main file

if true
X0 = rho;  % Make a starting guess at the solution
options = optimoptions('fsolve','Display','iter'); % Option to display output
[X,fval,exitflag,output] = fsolve(@eqDFT,X0,options); % Call solver
rho=X;
end
m -file for the first fsolve

if true
function  F=eqDFT(X)
Y0 = [alpha1 alpha2];  % Make a starting guess at the solution
options = optimoptions('fsolve','TolFun',1.e-12,'Display','iter'); % Option to display output
Y = fsolve(@eqAlpha,Y0,options,X); % Call solver
....
end
and the second fsolve @eqAlpha with Y variable and additionnal parameter X which is defined by rho like that

if true
  function G=eqAlpha(Y,rho)
  ....
  end
end

Thank you so much for reading this question and give me some ideas about it.

Answer 1

[Alan Weiss]

I am not sure that I understand you. How many times do you want to run fsolve? I suppose that you have a sequence of equations to solve, where each differs from the previous by a little bit, so the solution to the previous equation is a good starting guess for the next.

All you have to do is to use the previous solution x as the x0 input for fsolve. Something like

 x0 = rho
 for ii = 1:15
   x = fsolve(fun,x0);
   % change the parameters for fun here
   x0 = x; % update x0
 end

Alan Weiss

MATLAB mathematical toolbox documentation

[Vanduy TRAN]

Hi Alan,

I need to solve two non-linear systems A and B by fsolve. A is describeb by

if true
  X=fsolve(@fun(X,a),X0)
end

B is describeb by

if true
  [a,Y]=fsolve(@func(Y,X),Y0);
end

I want that when i run fsolve to solve A in na iterations, at each iteration, i take X to pass into fsolve of B as a output, and passing back from fsolve of B parameter a into fsolve of A for the next iteration of A. My problem is programed by the following codes.

if true
  X0; % initial guess
  a;
  for i=1:na,
  X(i)=fsolve(@fun(X(i),a),X0)
  [a,Y]=fsolve(@func(Y,X(i)),Y0);
  X0=X(i); %update X0
  Y0=Y; % update Y0
end
Do you have any idea?
Thank you so much :)

[Alan Weiss]

What you are doing looks reasonable in some sense. But some of the details are not clear to me.

When you call

 [a,Y]=fsolve(@func(Y,X(i)),Y0);

the returned Y will almost certainly be a vector of zeros, or a vector with very small elements. Is that what you want?

Alan Weiss

MATLAB mathematical toolbox documentation