おまけ. 速度比較

K6-2 450MHz. octave with atlas での結果.

octave:48> a=rand(1000,1000);
octave:49> b=rand(1000,1);
octave:50> tic;c=a\b;toc
ans = 23.848
octave:51> tic;c2=inv(a)*b;toc
ans = 65.178
octave:52> tic;[l u p]=lu(a);c2=u\(l\(p*b));toc
ans = 33.543
octave:53> tic;c2=u\(l\(p*b));toc
ans = 24.687
octave:3> tic;[l u p]=lu(a);c2=p*b;c2=l\c2;c2=u\c2;toc
ans = 33.223
octave:4> tic;[l u p]=lu(a);c3=p*b;c4=l\c3;c2=u\c4;toc
ans = 33.122
octave:6> tic;c2=p*b;c2=l\c2;c2=u\c2;toc
ans = 24.668

Celeron 433MHz with Atlas の場合:

octave:1> tic;a=rand(1000,1000);b=rand(1000,1);c=a\b;toc 
ans = 25.545
octave:2> tic;c=a\b;toc
ans = 23.402
octave:3> d=rand(1000,1000);
octave:4> tic;e=a*d;toc
ans = 6.7810
octave:3> tic;[l u p]=lu(a);c=u\(l\(p*b));toc
ans = 28.705