Computational time of qr, svd and eig?
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How does the time for qr depend on the dimensions of the matrix m and n (does it depend on on the type of linear systems: overdetermined and underdetermined?) How about svd and eig? Does the time depend on whether you ask only for the eigenvalues (as in E=eig(A)) or also for the eigenvectors (as in [V,E]=eig(A))?
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KSSV
on 3 May 2019
%% Computational time for qr.
clear all; clc; close all;
m = 700;
n = 500;
N = 100 ;
t11 = zeros(N,1) ;
t21 = zeros(N,1) ;
for k = 1:N
B1 = randn(m,n); % m>n
B2 = randn(n,m); % m<n
t10 = tic;
[Q1,R1] = qr(B1);
t11(k) = toc(t10);
t20 = tic;
[Q2,R2] = qr(B2);
t21(k) = toc(t20);
end
mean(t11)
mean(t21)
j = 1:N;
figure(1);
plot(j,t11,'r',j,t21,'b')
xlabel('# of trial')
ylabel('Elapsed time')
legend('qr for m<n','qr for m>n')
axis([0 100 0 0.05])
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