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I need to write a function MySolve

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sarah
sarah 2011-3-11
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 个评论
Andrew Newell
Andrew Newell 2011-3-11
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.

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回答（3 个）

Matt Tearle
Matt Tearle 2011-3-11
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 个评论
显示 1更早的评论
Andrew Newell
Andrew Newell 2011-3-11
@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
Matt Tearle 2011-3-11
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.

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Sean de Wolski
Sean de Wolski 2011-3-11
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
Joe Howes
Joe Howes 2012-5-10
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 个评论
Walter Roberson
Walter Roberson 2012-5-10
Do you want discussion here or in your Question on this topic, http://www.mathworks.com/matlabcentral/answers/38031-mysolve-help
Geoff
Geoff 2012-5-10
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.

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