LU分解（Doolittle分解）解线性方程组（Matlab版）

 

%LU分解，Doolittle分解

%L为单位下三角阵，U为上三角阵

clear;clc;

A=[3 -5 6 4 -2 -3 8;   

    1 1 -9 15 1 -9 2;

    2 -1 7 5 -1 6 11;  

    -1 1 3 2 7 -1 -2;

    4 3 1 -7 2 1 1;   

    2 9 -8 11 -1 -4 -1;

    7 2 -1 2 7 -1 9];%系数矩阵

b=[11 2 29 9 5 8 25]';%n维向量

% A=[4,-2,0,4;-2,2,-3,1;0,-3,13,-7;4,1,-7,23];

% b=[1 2 3 4];

n=length(b);%方程个数n

x=zeros(n,1);%未知向量

A(2:n,1)=A(2:n,1)./A(1,1);

for i=2:n-1

    A(i,i)=A(i,i)-sum(A(i,1:i-1)'.*A(1:i-1,i));

    for j=i+1:n

        A(i,j)=A(i,j)-sum(A(i,1:i-1)'.*A(1:i-1,j));

        A(j,i)=(A(j,i)-sum(A(j,1:i-1)'.*A(1:i-1,i)))/A(i,i);

    end

end

A(n,n)=A(n,n)-sum(A(n,1:n-1)'.*A(1:n-1,n));

A

U=A;L=A;

for i=1:n

    L(i,i)=1;

end

for i=1:n-1

    for j=i+1:n

        L(i,j)=0;

    end

end

L %下三角阵

for i=2:n

    for j=1: