I need to write a function MySolve

I need to write a function MySolve that will solve the nonlinear system of equations in the form

0=f(x)

where I have f:R^n -> R^n is an arbitrary function with n-dimensions input and n-dimensional output. The function should implement the newton iteration.

I know the first line of my function looks like:

function [x,converged]=MySolve(f,xo,tol,maxit)

But I am having difficulty with the rest

No one is going to do your homework for you. Try solving this problem yourself first, then show us your code and tell us what problems you're having.

Answer 1

function [x,converged]=MySolve(f,xo,tol,maxit)
opts = optimset('MaxIter',maxit,'TolFun',tol);
[x,~,converged] = fsolve(f,xo,opts);

(Unless, of course, this is a homework problem. In which case you might not be allowed to do that.)

Excellent Matt!

@Matt, I'm afraid I'll have to dock you some marks for using the the trust-region dogleg algorithm instead of a Newton method.

It's a fair cop. I was too lazy to look up which method fsolve used by default. From memory, I thought it was Levenburg-Marquardt. Which would count as a Newton method. Maybe it's fzero that uses Lev-Marq.

Answer 2

This should help a little

 while the_error > tol && iter <=  maxit
    iter = iter+1;
    Do a whole bunch of other stuff that you have to write
 end

Answer 3

i am also having the same problem as this so far i have

function [x,converged]=MySolve(f,xold,tol,maxit)

%maxit maximum number of iterations to be tried. 

x=xold;

h=1e-10;

% run a loop from 1 to maxit

for k=0:maxit  

%Need to call in MyJacobian   

J=Myjacobian(f,x,h);

% Newton iteration

x= xold-(J\f(xold));

if(max(abs(x-xold)))<tol && (max(abs(x-xold)))<tol
   converged=1;

   % Newtons iteration has converged

else
   converged=0;

   %Newtons iteration hasn't converged

end

xold=x;

end

end

with my jacobian function looking like this 

function df=Myjacobian(f,x,h)

% f: function to be differentiated
%x: point where jacobian is taken
% h: parameter for finite differences
% outputs df: m*n matrix, jacobian of f in x.

n=length(x); 

% defines number of rows 

fx=f(x);    
m=length(fx);

   % defines number of colums

df=zeros(n,m); 

% matrix of zeros 

      for i=1:n; 

          % runs a loop that takes two values x1 and x2 and places it
          % into my empty matrix df the process then produces 2 matircies of 
          % df1 and df2

         x(i)=x(i)+h;
          x1= f(x);
          x(i)=x(i)-(2*h);
          x2= f(x);
      df(:,i)=(x1-x2)/(2*h);
      x(i)=x(i)+h;

      end 

end

Do you want discussion here or in your Question on this topic, http://www.mathworks.com/matlabcentral/answers/38031-mysolve-help

Haha, yeah just gave a bunch of suggestions on that. Hopefully not too much =)

Just direct the whole class to this site. Your tutor would be so impressed.