MATLAB Central Newsreader - Fixed point Iteration (multivariable) 2

Fixed point Iteration (multivariable) 2

Sean Douglas — Thu, 02 Jul 2009 17:15:21 -0400

Hello I am trying to perform fixed point iteration on this problem:
x1=g1(x1,x2)=(x1^2+x2^2+8)/10, x2=g2(x1,x2)=(x1*x2^2+x1+8)/10

first I made it one variable since I am x1 and x2 will be equal to each other anyways. Here is my mfile:
%Computes approximate solution of g(x)=x
%Input: inline function g, starting guess x0,
% number of steps k
%Output: Approximate solution xc
function xc=fpi(g,x0,k)
x(1)=x0;
for i=1:k
  x(i+1)=g(x(i));
end
x' %transpose output to a column
xc=x(k+1);

then I defined x and did the inline function:
>> clear
>> x=-10:.001:10;
>> x=fpi(inline('((x.^2+x.^2+8)/10)'),.5,2)

ans =

    0.5000
    0.8500
    0.9445

x =

0.9445 this worked nicely

Now I am trying to do this how the question was set up (with mulivariables). I changed my mfile and tried to do it. Here is what I have been up to:
First here is my new modified mfile:
%Attempting to set up multivariable Fixed-Point Iteration
%Computes approximate solution of g(x)=x
%Input: inline function g, starting guess x0,
% number of steps k
%Output: Approximate solution xc
function xc=fpi(g,x0,y0,k)
x(1)=(x0,y0);
for i=1:k
  x(i+1)=g(x(i),y(i));
end
x' %transpose output to a column
xc=x(k+1);

… and here is me calling the function and the MATLAB response
>> clear
x=-10:.001:10;
y=-10:.001:10;
>> x=fpixy(inline('((x.^2+y.^2+8)/10)'),.5,.5,2)
??? Error: File: fpixy.m Line: 7 Column: 9
Expression or statement is incorrect--possibly unbalanced (, {, or [.

I am pretty sure that it is not unbalaced, but something must be wrong with line 7 of my mfile, which is: x(1)=(x0,y0);

Can I even do a multivariable FPI?
I hope I described my situation clearly. Thanks for any help.

Re: Fixed point Iteration (multivariable) 2

Steve Conahan — Thu, 02 Jul 2009 19:58:53 -0400

Hi Sean,

> ??? Error: File: fpixy.m Line: 7 Column: 9

As indicated, Line: 7 needs some re-writing:

x(1)=(x0,y0);

I am not exactly sure what you are trying to do, but I suspect that the
right hand side of the above equation is not written correctly...perhaps you
need square braces [ instead of parentheses ( on the right hand side...

hth,
Steve

"Sean Douglas" <seanjdouglas@hotmail.com> wrote in message
news:h2ipv9$h8m$1@fred.mathworks.com...
> Hello I am trying to perform fixed point iteration on this problem:
> x1=g1(x1,x2)=(x1^2+x2^2+8)/10, x2=g2(x1,x2)=(x1*x2^2+x1+8)/10
>
> first I made it one variable since I am x1 and x2 will be equal to each
> other anyways. Here is my mfile:
> %Computes approximate solution of g(x)=x
> %Input: inline function g, starting guess x0,
> % number of steps k
> %Output: Approximate solution xc
> function xc=fpi(g,x0,k)
> x(1)=x0;
> for i=1:k
> x(i+1)=g(x(i));
> end
> x' %transpose output to a column
> xc=x(k+1);
>
> then I defined x and did the inline function:
>>> clear
>>> x=-10:.001:10;
>>> x=fpi(inline('((x.^2+x.^2+8)/10)'),.5,2)
>
> ans =
>
> 0.5000
> 0.8500
> 0.9445
>
>
> x =
>
> 0.9445 this worked nicely
>
>
> Now I am trying to do this how the question was set up (with
> mulivariables). I changed my mfile and tried to do it. Here is what I have
> been up to:
> First here is my new modified mfile:
> %Attempting to set up multivariable Fixed-Point Iteration
> %Computes approximate solution of g(x)=x
> %Input: inline function g, starting guess x0,
> % number of steps k
> %Output: Approximate solution xc
> function xc=fpi(g,x0,y0,k)
> x(1)=(x0,y0);
> for i=1:k
> x(i+1)=g(x(i),y(i));
> end
> x' %transpose output to a column
> xc=x(k+1);
>
> … and here is me calling the function and the MATLAB response
>>> clear
> x=-10:.001:10;
> y=-10:.001:10;
>>> x=fpixy(inline('((x.^2+y.^2+8)/10)'),.5,.5,2)
> ??? Error: File: fpixy.m Line: 7 Column: 9
> Expression or statement is incorrect--possibly unbalanced (, {, or [.
>
> I am pretty sure that it is not unbalaced, but something must be wrong
> with line 7 of my mfile, which is: x(1)=(x0,y0);
>
> Can I even do a multivariable FPI?
> I hope I described my situation clearly. Thanks for any help.

Re: Fixed point Iteration (multivariable) 2

Sean Douglas — Thu, 02 Jul 2009 20:37:01 -0400

Thank you very much for response - just giving me new ideas helps alot.

square brackets[] will turn it into a matrix, I dont know if I want that even though the output get transposed at the end of the mfile.

BTW I did not need to use square brackets when I did the single variable problem that i put as an example in my previous question.
I dont know yet though, you may be on to something

thanks Steve

"Steve Conahan" <sconahan@mathworks.com> wrote in message <h2j3hu$mq4$1@fred.mathworks.com>...
> Hi Sean,
>
> > ??? Error: File: fpixy.m Line: 7 Column: 9
>
> As indicated, Line: 7 needs some re-writing:
>
> x(1)=(x0,y0);
>
> I am not exactly sure what you are trying to do, but I suspect that the
> right hand side of the above equation is not written correctly...perhaps you
> need square braces [ instead of parentheses ( on the right hand side...
>
> hth,
> Steve
>
>
> "Sean Douglas" <seanjdouglas@hotmail.com> wrote in message
> news:h2ipv9$h8m$1@fred.mathworks.com...
> > Hello I am trying to perform fixed point iteration on this problem:
> > x1=g1(x1,x2)=(x1^2+x2^2+8)/10, x2=g2(x1,x2)=(x1*x2^2+x1+8)/10
> >
> > first I made it one variable since I am x1 and x2 will be equal to each
> > other anyways. Here is my mfile:
> > %Computes approximate solution of g(x)=x
> > %Input: inline function g, starting guess x0,
> > % number of steps k
> > %Output: Approximate solution xc
> > function xc=fpi(g,x0,k)
> > x(1)=x0;
> > for i=1:k
> > x(i+1)=g(x(i));
> > end
> > x' %transpose output to a column
> > xc=x(k+1);
> >
> > then I defined x and did the inline function:
> >>> clear
> >>> x=-10:.001:10;
> >>> x=fpi(inline('((x.^2+x.^2+8)/10)'),.5,2)
> >
> > ans =
> >
> > 0.5000
> > 0.8500
> > 0.9445
> >
> >
> > x =
> >
> > 0.9445 this worked nicely
> >
> >
> > Now I am trying to do this how the question was set up (with
> > mulivariables). I changed my mfile and tried to do it. Here is what I have
> > been up to:
> > First here is my new modified mfile:
> > %Attempting to set up multivariable Fixed-Point Iteration
> > %Computes approximate solution of g(x)=x
> > %Input: inline function g, starting guess x0,
> > % number of steps k
> > %Output: Approximate solution xc
> > function xc=fpi(g,x0,y0,k)
> > x(1)=(x0,y0);
> > for i=1:k
> > x(i+1)=g(x(i),y(i));
> > end
> > x' %transpose output to a column
> > xc=x(k+1);
> >
> > … and here is me calling the function and the MATLAB response
> >>> clear
> > x=-10:.001:10;
> > y=-10:.001:10;
> >>> x=fpixy(inline('((x.^2+y.^2+8)/10)'),.5,.5,2)
> > ??? Error: File: fpixy.m Line: 7 Column: 9
> > Expression or statement is incorrect--possibly unbalanced (, {, or [.
> >
> > I am pretty sure that it is not unbalaced, but something must be wrong
> > with line 7 of my mfile, which is: x(1)=(x0,y0);
> >
> > Can I even do a multivariable FPI?
> > I hope I described my situation clearly. Thanks for any help.
>