Re: norm of sparse matrices

[Jordi Gutiérrez Hermoso]

On 25 November 2011 06:10, c. <address@hidden> wrote:
>
> On 25 Nov 2011, at 11:00, Marco Caliari wrote:
>
>> Dear users,
>>
>> anybody knows which algorithm is used to compute the Euclidean norm of a 
>> sparse matrix? An iterative method with a random initial value (such as in 
>> normest)? Because I sometimes see different results on the same matrix:
>>
>> octave:39> S=sprand(5,5,0.5);
>> octave:40> norm(S)
>> ans =  1.08208354239579e+00
>> octave:41> norm(S)
>> ans =  1.08208354232114e+00
>> octave:42> norm(S)
>> ans =  1.08208354232114e+00
>>
>> (not easy to reproduce this behaviour). I'm using 3.4.1.
>>
>> Cheers,
>>
>> Marco
>
> Looking at the comments in the source code at
> http://hg.savannah.gnu.org/hgweb/octave/file/c3c8f513cf1f/liboctave/oct-norm.cc#l317
> http://hg.savannah.gnu.org/hgweb/octave/file/c3c8f513cf1f/liboctave/oct-norm.cc#l408
>
> it refers to "Higham's method" which I guess is the one described here
> http://www.springerlink.com/content/vh62v0354536p236/
>
> but I'm not an expert on the topic so I cannot help further.

It appears this is correct. I have added the reference to the source:

    http://hg.savannah.gnu.org/hgweb/octave/rev/7a756a7e145b

If you have difficulty accessing the paper, I have a copy that I may
lend to anyone who asks.

Thanks,
- Jordi G. H.