改进的平方根法

改进的平方根法A= L*D*L'的Matlab程序function [L,D]=LDLT(A)

%improve square decomposition A=L*D*L'

%for symmetric positive definite matrix

%L is lower triangle matrix,D is scale matrix

n=length(A);

%判断矩阵是否对称，不对称时退出程序并提示

sj=A'-A;

tsj=all(sj(:));

iftsj~=0

error('A is not a symmetric matrix.');

end

L=eye(n);

D=diag(L);

%采用向量化编程

for k=1:n

for l=1:k-1

L(k,l)=(A(k,l)-(L(k,1:l-1).*D(1:l-1)')*L(l,1:l-1)')/D(l);

end

D(k)=A(k,k)-(L(k,1:k-1).*L(k,1:k-1))*D(1:k-1);

end

D=diag(D);