施密特正交化QR分解求逆矩阵与MATLAB仿真

clc; clear all; close all; N=4:1:16; time=zeros(1,length(N)); error=zeros(1,length(N)); cheng=zeros(1,length(N)); jia=zeros(1,length(N)); chu=zeros(1,length(N)); for a=1:length(N) A = randn(N(a), N(a))+1i*randn(N(a), N(a)); % 生成一个随机矩阵 for b=1:20 tic [Q, R] = fx_QR_decom(A); R_inv = fx_inverse_upper_triangular_matrix(R); %求三角矩阵的逆 A_inv = R_inv*Q'; time(a)=time(a)+toc; error(a)=error(a)+sum(sum(abs(A_inv-inv(A)))); end cheng(a)=(10*N(a).^3+9*N(a).^2-N(a))/6; jia(a)=(13*N(a).^3-12*N(a).^2-N(a))/6; chu(a)=(3*N(a).^2+N(a))/2; time(a)=time(a)/20; error(a)=error(a)/20; end figure(1); plot(N,error,LineWidth=1.5,Marker="*"); title("schmidt QR分解求逆仿真"); xlabel("矩阵阶数"); ylabel("计算误差"); figure(2); plot(N,time,LineWidth=1.5,Marker="*"); title("schmidt QR分解求逆仿真"); xlabel("矩阵阶数"); ylabel("计算时间"); figure(3); plot(N,cheng,N,jia,N,chu,LineWidth=1.5,Marker="*"); legend("乘法","加法","除法"); title("schmidt QR分解求逆仿真"); xlabel("矩阵阶数"); ylabel("运算次数");