|Re: [eigen] Student contribution|
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- To: eigen <eigen@xxxxxxxxxxxxxxxxxxx>
- Subject: Re: [eigen] Student contribution
- From: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>
- Date: Sun, 16 Jun 2013 17:26:46 -0400
- Cc: simon.courtemanche@xxxxxxxx, Pierre ZOPPITELLI <Pierre.Zoppitelli@xxxxxxxxxxxxxxx>, Nicolas Carré <carren@xxxxxxxxxxxxxx>, Jean CECCATO <Jean.Ceccato@xxxxxxxxxxxxxxx>
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There is also a particular point that I should elaborate on:
If there existed such a thing as a 1.7x speed improvement over JacobiSVD with no downsides, of course we would want to include it. (Such a thing might actually exist, by the way, by making JacobiSVD blocked).
The problem is that bidiagonalization means that we lose the accuracy characteristics of JacobiSVD.
There are two usual kinds of SVD algorithms (at least, for the purpose of this conversation):
- Jacobi SVD, which is accurate but slow,
- Bidiagonalizing SVD, which is (relatively) inaccurate but fast
The question becomes whether there are sufficient use cases for a Jacobi algorithm that has accuracy characteristics comparable to other bidiagonalizing SVD's, while being slower than typical bidiagonalizing SVD's.