Re: [eigen] BDCSVD update |

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*To*: eigen <eigen@xxxxxxxxxxxxxxxxxxx>*Subject*: Re: [eigen] BDCSVD update*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Tue, 20 Aug 2013 17:16:14 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-type; bh=ypQ3cwC092jufFP+F1CrIWfIB+94GXBAdw38sGBjkP8=; b=AWnatPhaGbZvu93YG7SljIJpXtBm67GUp8I3Ck2V2EVo+WGYhCTFJDjBxFcrubdSWf JX2oWWFToykCQbCG3/vTLaA/xKJ6fNXK6XPzPCxvi4sD8ZiHWSBE4YwPe1SLcPjbOtBG GR9hxUOYe7I39x0Yomwu0RxXgR/g3I8VKMiyHZr+GRwXPtQ6xWm3VAFBo7LIMw+qMH66 pTvtX+jb3IuydCc5whcR4FyC3GJljid0g7HGeNAy126XXlU3JIFEmhwKtsr6jq3D+ph8 44pSTi3cvPhGt0KG4UXU6TK3jcye3oekoHzJ2gaFuU04HKaaniNG/cHwjL2Sdo6FDK0h B+sw==

excellent!

Lapack is using rational approximations to help solving the non-linear equation. There is also this paper [1] that suggest using the fast-multipole-method, but before moving to other algorithms we should make some performance analysis to see how far we can get with that one.

gael

On Tue, Aug 20, 2013 at 3:34 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:

Benoit\o/Thanks Jitse, that's very useful work!

2013/8/20 Jitse Niesen <jitse@xxxxxxxxxxxxxxxxx>

Hello,

I continued work on the BDCSVD (bidiagonalizing divide-and-conquer SVD), building on the excellent work of the group of students at ensimag in Grenoble. The basic algorithm is now fully implemented. It took me longer than expected; small mistakes and short-cuts that I took lead to loss of accuracy. However, at the moment all tests pass, it seems accurate on random matrices, and it's faster than JacobiSVD (about a factor of four for a 160-by-160 matrix).

I used the bisection method to solve the nonlinear equation at the heart of the algorithm, which is hardly state-of-the-art. In fact, I think most of the lines of code I added can be improved, so I intend to spend some time optimizing and fine-tuning the BDCSVD class.

Thanks again to Gauthier, Ncolas, Jean and Pierre for their work. Their well-documented code and their report made it easy for me to get started.

Jitse

**Follow-Ups**:**Re: [eigen] BDCSVD update***From:*Gael Guennebaud

**Re: [eigen] BDCSVD update***From:*Jitse Niesen

**References**:**[eigen] BDCSVD update***From:*Jitse Niesen

**Re: [eigen] BDCSVD update***From:*Benoit Jacob

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