qr_algrithm.asv

求矩阵特征值和特征向量的算法：QR算法。用于线性方程组的求解

            function [A2]=QR_algrithm(A,N)
            k=1;while k<N
            [Q,R]=Gram_Schemidt(A);
            A2=R*Q;
            k=1+k;A=A2;
            end
            end
            % A=[2,-1,0;-1,2,-1;0,-1,2];
            % %A=[5,-2,-5,-1;1,0,-3,2;0,2,2,-3;0,0,1,-2];
            % N=16;
            % [A2]=QR_algrithm(A,N)
            %-------------------------------------------
            % function [Q,R]=Gram_Schemidt(A)
            % [m,n]=size(A);beta=zeros(m,n);R=zeros(m,n);
            % R(1,1)=norm(A(:,1),2);
            % beta(:,1)=A(:,1)/R(1,1);
            % Q=[beta(:,1)];
            % for j=2:n
            %     for k=1:j-1
            %     R(k,j) =beta(:,k)'*A(:,j);
            %     beta(:,j)=A(:,j)-R(k,j)*beta(:,k);
            %     A(:,j)=beta(:,j);
            %     end
            %     R(j,j)=norm(beta(:,j),2);
            %     beta(:,j)=beta(:,j)/R(j,j);
            %     Q=[Q beta(:,j)];    
            % end
            % end
            % % clc
            % % clear
            % % A=[5 -2 -5 -1;1 0 -3 2;0 2 2 -3;0 0 1 -2];
            % % [Q,R]=Gram_Schemidt(A)