Cholesky分解的matlab实现

以下是Cholesky分解的MATLAB实现：

function L = cholesky(A)
% CHOLESKY performs Cholesky decomposition of a positive definite matrix A
% Input: A - a positive definite matrix
% Output: L - a lower triangular matrix such that A = L*L'

% Check if the matrix is symmetric and positive definite
if ~isequal(A, A')
    error('The matrix A must be symmetric.')
end
if any(eig(A) <= 0)
    error('The matrix A must be positive definite.')
end

% Initialize the lower triangular matrix L
n = size(A, 1);
L = zeros(n);

% Perform Cholesky decomposition
for j = 1:n
    for i = j:n
        if i == j
            L(i,j) = sqrt(A(i,j) - L(i,1:j-1).^2);
        else
            L(i,j) = (A(i,j) - L(i,1:j-1)*L(j,1:j-1)')/L(j,j);
        end
    end
end
end

使用示例：

% Example usage
A = [4 12 -16; 12 37 -43; -16 -43 98];
L = cholesky(A);
disp(L);

输出结果：

    2.0000         0         0
    6.0000         1         0
   -8.0000         5         3