基于MATLAB的Cholesky分解法（by Violet）

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Method

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Let L=⎡⎣⎢⎢⎢⎢⎢l11l21⋮ln10l22⋮ln2⋯ ⋯ ⋱⋯ 00⋮lnn⎤⎦⎥⎥⎥⎥⎥
Use Squre Root Method, when A=LLT, we have:

uii=aii−∑k=1i−1u2ki−−−−−−−−−−⎷,i=1,…,n

uij=aij−∑i−1k=1uikujkuii,j=i+1,…,n

Using these two function to realize Cholesky factorization.

function [L]=Cholesky(A)   %平方根法    [N,N]=size(A);    X=zeros(N,1);    Y=zeros(N,1);    for i=1:N        A(i,i)=sqrt(A(i,i)-A(i,1:i-1)*A(i,1:i-1)');        if A(i,i)==0            'A is singular, no unique solution';            break;        end        for j=i+1:N            A(j,i)=(A(j,i)-A(j,1:i-1)*A(i,1:i-1)')/A(i,i);        end    endfor x=1:N    for y=1:N        B(x,y)=A(x,y);      %右上角元素归0        if x<y            B(x,y)=0;            break;        end    endendL=B