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function [T, P] = householder(A) % Formations: RA = T, where A is original matrix % The implementation of Householder Reduction % R is constructed as a product of elementary reflector % T is upper tri

function [P, L, U] = plu(A) % The implementation of PLU Factorization % L is lower triangular and U is upper triangular % P is permutation matrix % Author: Zhenlin Du(Johnsondu) % Email: qlduzhlin@

PLU分解的好处是，可以将Ax=b的矩阵，转换成Ly=b, Ux = y 的形式，当我们改变系数矩阵b时，此时由于矩阵L和U均是固定 的，所以总能高效的求出矩阵的解。 // LU.cpp : Defines the entry point for the console application. // /********************************************

function [Q,R] = gram_schmidt_qr(A) % Formation: A = QR % The implementation of QR Factorization(classical Gram-Schmidt method) % Q is orthonormal basis for R(A) % R is an upper-triangular matrix wit