gauseid.m

辛普森方法

function X = gauseid(A,B,X0,kmax)
%This function finds a soltuion to AX= B by Gauss–Seidel iteration.

if nargin < 4
	tol = 1e-6; kmax = 100;                       %called by gauseid(A,B,X0)
elseif kmax < 1
	tol = max(kmax,1e-16); kmax = 1000; %called by gauseid(A,B,X0,tol)
else 
	tol = 1e-6;                                           %called by gauseid(A,B,X0,kmax)
end

if nargin < 3, X0 = zeros(size(B)); end       %called by gauseid(A,B)

NA = size(A,1);
X = X0;

for k = 1: kmax
    X(1,:) = (B(1,:)-A(1,2:NA)*X(2:NA,:))/A(1,1);
    for m = 2:NA-1
        tmp = B(m,:)-A(m,1:m-1)*X(1:m - 1,:) - A(m,m + 1:NA)*X(m + 1:NA,:);
        X(m,:) = tmp/A(m,m); 
    end
    X(NA,:) = (B(NA,:)-A(NA,1:NA - 1)*X(1:NA - 1,:))/A(NA,NA);
    if nargout == 0, X, end %To see the intermediate results
    if norm(X - X0)/(norm(X0) + eps)<tol, break; end
    X0 = X;
end