Re: Improved normest

[David Bateman]

Jaroslav Hajek wrote:
> I see, thanks. I randomized the guess again. My problem with the previous
> code was that a priori forming A'*A is quite costly, especially if you want
> just low precision and expect just a dozen iterations:
>
> A = rand (1e3);
> tic; [e,c] = normest (A); toc
> tic; [e,c] = normest (A, 1e-1); toc
>
> now:
>
> Elapsed time is 0.0229969 seconds.
> Elapsed time is 0.0183249 seconds.
>
> previously:
>
> Elapsed time is 0.220653 seconds.
> Elapsed time is 0.210241 seconds.
>   
Explicitly forming A'*A seemed the right thing to do for full matrices 
as it only needed to be done once. I suppose it only makes sense to do 
so in the case of difficult convergence.. In that case a similar issue 
probably exists in the code bicgstab where is two preconditioning 
matrices are given then

precon = @(x) M2 \ (M1 \ x);

if M1 and M2 are sparse or

M = M1 \ M2;
precon @(x) M \ x;

otherwise. Though bicgstab usually has many more iterations than a 
simple power method as in normest, so perhaps the existing code is the 
right ting to do..

D.

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