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

[Andrew Newell]

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

[Matt Tearle]

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.)

[Sean de Wolski]

Excellent Matt!

[Andrew Newell]

@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.

[Matt Tearle]

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

[Sean de Wolski]

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

[Joe Howes]

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

[Walter Roberson]

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

[Geoff]

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.