matlab 高斯迭代代码_超松弛迭代法（SOR）

好的，这是一个 Matlab 的超松弛迭代法（SOR）的高斯迭代代码，可以用于解决线性方程组：

function [x,iter]=SOR(A,b,x0,w,tol,maxiter)
% SOR(A,b,x0,w,tol,maxiter) uses the Successive Over-Relaxation method
% to solve the linear system Ax=b.
% Inputs:
%   A is an n x n matrix
%   b is an n x 1 vector
%   x0 is an n x 1 vector representing the initial guess
%   w is the relaxation parameter (default is w=1)
%   tol is the tolerance for stopping criteria (default is tol=1e-6)
%   maxiter is the maximum number of iterations (default is maxiter=100)
% Outputs:
%   x is an n x 1 vector representing the solution
%   iter is the number of iterations performed

% Check inputs and set default values
if nargin<3
    error('At least three inputs are required.')
end
if nargin<4 || isempty(w)
    w=1;
end
if nargin<5 || isempty(tol)
    tol=1e-6;
end
if nargin<6 || isempty(maxiter)
    maxiter=100;
end

% Initialize variables
n=length(b);
x=x0;
iter=0;
err=inf;

% Perform SOR iterations
while err>tol && iter<maxiter
    xold=x;
    for i=1:n
        x(i)=(1-w)*xold(i)+w*(b(i)-A(i,1:i-1)*x(1:i-1)-A(i,i+1:n)*xold(i+1:n))/A(i,i);
    end
    iter=iter+1;
    err=norm(x-xold)/norm(x);
end

% Display error message if maximum number of iterations is reached
if iter==maxiter && err>tol
    warning('Maximum number of iterations reached without convergence.')
end
end

其中，A 为系数矩阵，b 为常数向量，x0 为初始解向量，w 为松弛因子，tol 为迭代停止的相对误差，maxiter 为最大迭代次数。

示例用法：

% Example usage:
A=[4 -1 0 0; -1 4 -1 0; 0 -1 4 -1; 0 0 -1 3];
b=[15;10;10;10];
x0=[0;0;0;0];
w=1.25;
tol=1e-6;
maxiter=100;
[x,iter]=SOR(A,b,x0,w,tol,maxiter);
disp(['Solution: [',num2str(x.'),']'])
disp(['Number of iterations: ',num2str(iter)])

希望能对你有帮助！