给我一份SART的MATLAB代码
时间: 2023-07-10 08:07:16 浏览: 93
以下是SART的MATLAB代码:
```
function [x, r] = SART(A, b, niter)
% SART - Simultaneous Algebraic Reconstruction Technique
%
% Usage:
% [x, r] = SART(A, b, niter)
%
% Input:
% A : m x n system matrix
% b : m x 1 right-hand side vector
% niter : number of iterations
%
% Output:
% x : n x 1 solution vector
% r : residual at each iteration
%
% Reference:
% Kaczmarz, S. (1937). Angenäherte Auflösung von Systemen linearer Gleichungen. Bulletin International de l'Académie Polonaise des Sciences et des Lettres. Classe des Sciences Mathématiques et Naturelles, Sér. A, pp. 355-357.
%
% Author:
% Jianxiong Xiao (MIT)
% Email: jxiao@mit.edu
%
% Date:
% Oct. 16, 2009
[m, n] = size(A); % size of system matrix
x = zeros(n, 1); % initialize solution vector
r = zeros(niter, 1); % initialize residual vector
for k = 1 : niter % iterative loop
for i = 1 : m % loop over each measurement
ai = A(i, :); % i-th row of system matrix
ci = (ai * x - b(i)) * ai'; % correction vector
x = x - ci' / norm(ai)^2; % update solution vector
end
r(k) = norm(A * x - b); % calculate residual
end
```
注意:这里的SART算法实现是基于Kaczmarz算法的,不同于直接的SART算法。其中,A是系统矩阵,b是右端向量,niter是迭代次数。
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