Code covered by the BSD License

# Numerical Methods Using MATLAB, 4e

### John Mathews (view profile)

23 Dec 2003 (Updated )

Companion software to accompany the book "Numerical Methods Using MATLAB"

X=gseid(A,B,P,delta, max1)
```function X=gseid(A,B,P,delta, max1)

% Input    - A is an N x N nonsingular matrix
%             - B is an N x 1 matrix
%             - P is an N x 1 matrix; the initial guess
%	          - delta is the tolerance for P
%	          - max1 is the maximum number of iterations
% Output - X is an N x 1 matrix: the gauss-seidel approximation to
%	            the solution of AX = B

%  NUMERICAL METHODS: Matlab Programs
% (c) 2004 by John H. Mathews and Kurtis D. Fink
%  Complementary Software to accompany the textbook:
%  NUMERICAL METHODS: Using Matlab, Fourth Edition
%  ISBN: 0-13-065248-2
%  Prentice-Hall Pub. Inc.
%  One Lake Street
%  Upper Saddle River, NJ 07458

N = length(B);

for k=1:max1
for j=1:N
if j==1
X(1)=(B(1)-A(1,2:N)*P(2:N))/A(1,1);
elseif j==N
X(N)=(B(N)-A(N,1:N-1)*(X(1:N-1))')/A(N,N);
else
%X contains the kth approximations and P the (k-1)st
X(j)=(B(j)-A(j,1:j-1)*X(1:j-1)'-A(j,j+1:N)*P(j+1:N))/A(j,j);
end
end
err=abs(norm(X'-P));
relerr=err/(norm(X)+eps);
P=X';
if (err<delta)|(relerr<delta)
break
end
end

X=X';

```