Re: mgorth usage

[JuanPi]

On Mon, Sep 17, 2012 at 9:32 PM, c. <address@hidden> wrote:
>
> On 17 Sep 2012, at 21:28, c. wrote:
>
>>
>> On 17 Sep 2012, at 18:29, Jordi Gutiérrez Hermoso wrote:
>>
>>> Gram-Schmidt is numerically unstable, so there's no reason for Octave
>>> to have it. Instead, use orth, which uses the svd.
>>
>> Gram-Schmidt is numerically unstable, that's why mgorth uses _modified_ 
>> Gram-Schmidt which is more stable.
>> THERE IS reason to have mgorth as it is a required step in any algorithm 
>> based on the Arnoldi process [1],
>> like, for example, GMRES [2].
>>
>>> HTH,
>>> - Jordi G. H.
>> c.
>>
>> [1] http://en.wikipedia.org/wiki/Arnoldi_iteration
>> [2] http://en.wikipedia.org/wiki/Generalized_minimal_residual_method
>
> jordi,
>
> reading your message again I see I had initially erroneously interpreted it
> as suggesting that Octave does not need mgorth. I now understand this was not
> the case, sorry for the noise. Hope the references on "mgorth"'s algorithm are
> of use to JP anyway.
>
> c.

Thanks again, all very useful!


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