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I need to write a function MySolve

Asked by sarah on 11 Mar 2011

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

1 Comment

Andrew Newell on 11 Mar 2011

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.

sarah

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3 Answers

Answer by Matt Tearle on 11 Mar 2011
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.)

3 Comments

Sean de Wolski on 11 Mar 2011

Excellent Matt!

Andrew Newell on 11 Mar 2011

@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 on 11 Mar 2011

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.

Matt Tearle
Answer by Sean de Wolski on 11 Mar 2011

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

0 Comments

Sean de Wolski
Answer by Joe Howes on 10 May 2012

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

2 Comments

Walter Roberson on 10 May 2012

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

Geoff on 10 May 2012

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.

Joe Howes

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