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Topic: Problem with Newton Raphson Method for Two Variables
Replies: 5   Last Post: Jun 25, 2013 2:27 AM

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shubha22@gmail.com

Posts: 2
Registered: 6/24/13
Re: Problem with Newton Raphson Method for Two Variables
Posted: Jun 24, 2013 10:57 PM
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Hello Torsten

I'm trying to obtain the values for x1 and x2. Yes exactly, f1 only depends on x1 and f2 on x2, while x1 and x2 are dependent on each other. Since the two functions are non-linear, I use NR method to optimize until a certain tolerance limit.

Shubha

On Monday, June 24, 2013 6:03:09 PM UTC+5:30, Torsten wrote:
> shubha22@gmail.com wrote in message <5a7b5f15-296b-4133-9502-7cca0508ebf3@googlegroups.com>...
>

> > Hello,
>
> >
>
> > I have two functions, f1(x1)=a1*exp(b1*x1)
>
> > and f2(x2)=a2*exp(-((x2-b2)/c2)^2)
>
> > where a1, b1, a2, b2 and c2 are constants. x1 and x2 are dependent variables.
>
> > I need to solve the two functions using newton raphson's method. Can anyone help me?
>
> >
>
> > Thanks
>
> > Shubha
>
> >
>
> >
>
> > On Wednesday, October 12, 2011 2:50:30 PM UTC+5:30, Emre wrote:
>
> > > clc,clear
>
> > >
>
> > > % Newton Raphson solution of two nonlinear algebraic equations
>
> > >
>
> > > % set up the iteration
>
> > >
>
> > > error1 = 1.e8;
>
> > >
>
> > > xx(1) = 0; % initial guesses
>
> > >
>
> > > xx(2) = 0.5;
>
> > >
>
> > > iter=0;
>
> > >
>
> > > maxiter=40
>
> > >
>
> > > % begin iteration
>
> > >
>
> > > while error1>1.e-12
>
> > >
>
> > > iter=iter+1;
>
> > >
>
> > > x = xx(1);
>
> > >
>
> > > y = xx(2);
>
> > >
>
> > > % calculate the functions
>
> > >
>
> > > f(1) = 4*x^2-20*x+0.25*y^2+8;
>
> > >
>
> > > f(2) = 0.5*x*y^2+2*x+8;
>
> > >
>
> > > % calculate the Jacobian
>
> > >
>
> > > J(1,1) = 8*x-20;
>
> > >
>
> > > J(1,2) = 0.5*y;
>
> > >
>
> > > J(2,1) = 0.5*y^2+2;
>
> > >
>
> > > J(2,2) = x*y;
>
> > >
>
> > > % solve the linear equations
>
> > >
>
> > > y = -J\f';
>
> > >
>
> > > % move the solution, xx(k+1) - xx(k), to xx(k+1)
>
> > >
>
> > > xx = xx + y';
>
> > >
>
> > > % calculate norms
>
> > >
>
> > > error1=sqrt(y(1)^2+y(2)^2);
>
> > >
>
> > > error(iter)=sqrt(f(1)^2+f(2)^2);
>
> > >
>
> > > ii(iter)=iter;
>
> > >
>
> > > if (iter > maxiter)
>
> > >
>
> > > error1 = 0;
>
> > >
>
> > > s=sprintf('****Did not converge within %3.0f iterations.****',maxiter);
>
> > >
>
> > > disp(s)
>
> > >
>
> > > end
>
> > >
>
> > > % check if error1 < 1.e-12
>
> > >
>
> > > end
>
> > >
>
> > > x = xx(1);
>
> > >
>
> > > y = xx(2);
>
> > >
>
> > > f(1) = 4*x^2-20*x+0.25*y^2+8;
>
> > >
>
> > > f(2) = 0.5*x*y^2+2*x+8;
>
> > >
>
> > > % print results
>
> > >
>
> > > f
>
> > >
>
> > > xx
>
> > >
>
> > > iter
>
> > >
>
> > > % plot results
>
> > >
>
> > > semilogy(ii,error)
>
> > >
>
> > > xlabel('iteration number')
>
> > >
>
> > > ylabel('norm of functions')
>
> > >
>
> > > clear ii
>
> > >
>
> > > clear error
>
> > >
>
> > >
>
> > >
>
> > > what am i doing wrong here, it doesn't converge and find the correct values for x and y?
>
> > >
>
> > > Is this part
>
> > >
>
> > > "error1=sqrt(y(1)^2+y(2)^2);
>
> > >
>
> > > error(iter)=sqrt(f(1)^2+f(2)^2);" right?
>
> > >
>
> > > Please help me, thanks.
>
>
>
> Except for trivial cases, both functions f1 and f2 don't have a zero.
>
> Moreover, f1 only depends on x1 and f2 only depends on x2.
>
> So what exactly are you trying to do with Newton-Raphson ?
>
>
>
> Best wishes
>
> Torsten.





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