Please help me transform Jacobi into Gauss-Seidel

Hello everybody...

To be honest, I am taking a linear algebra class (where the professor teaches and uses Matlab quite a bit). Not all of us took Matlab (but C programming, and long ago at that) and are at a big disadvantage trying to do his assignment. None of the other Linear Algebra professors use Matlab like he does, I figure, because it is one of his specialties.

Myself and a few fellow students were able to get this follow Jacobi program to run and work correctly... But now, we must transform into Gauss-Seidel and need help.

I honestly have no idea what I am doing... It also mentions something about Convergence Criteria and Relaxation in the Conversion, but not sure exactly what he means. He was poor at explaining.

I appreciate your help, very much. Information below.

-------------------------------

This was written to solve the following equations:

1.) 3X1 - 0.1X2 - 0.2X3 = 7.85

2.) 0.1X1 + 7X2 - 0.3X3 = -19.3

3.) 0.3X1 - 0.2X2 + 10X3 = 71.4

And Solutions are:

X1 = 3 X2 = -2.5 X3 = 7

------------------------

n=input('Dimension of system= ');

a=input('Coefficent matrix= ');

b=input('Solution vector= ');

x=input('Starting vector= ');

epsilon=input('Convergence criterion= ');

itmax=input('Maxinmum number of iterations= ');

%----------------------------------------------------

%Outer loop for Jacobi-iteration

maxerr=100;

it=0;

while maxerr>epsilon && it<itmax;

    it = it+1;
    xold=x;

%loop over all equations in system

    for i=1:n,

%loop to perform jacobi-sum

    sum = b(i);
    for j =1:n;

%skip over i = j

    if i~=j;
        sum=sum-a(i,j)*xold(j);
    end
    x(i)=sum/a(i,i);
    end
%compute current error
        if x(i)~=0;
    xerr(i)=abs((x(i)-xold(i))/x(i))*100;
        end
    end

%check for maximum error

maxerr=max(xerr);

end

%Show Solutions

fprintf('Number of Iternations=%8.3f\n',it);

fprintf('Maximum Error=%8.3f\n',maxerr);

disp('Solution Vector=');

disp(x)

Answer 1

[Matt Tearle]

So you keep a copy of x, called xold, which you use to calculate the new values of x. The main part of the algorithm happens on the line sum=sum-a(i,j)*xold(j)

The difference between Jacobi and GS is whether or not you use the new x values calculated so far in the current iteration. Given that you use xold to calculate sum, you're not using the new values...

I think that's about as big a hint as I can give without just telling you the answer!