| Re: [eigen] Instability in LLT and LDLT methods. |
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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] Instability in LLT and LDLT methods.
- From: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>
- Date: Wed, 28 Jan 2009 08:42:30 +0100
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yes, indeed with LDLt we could do full pivoting and be as stable as LU
for selfadjoint matrices while being faster. My initial motivation
with LDLt, however, was its performance because it avoids the square
roots... On the other hand, I remember my benchmark was not really in
favor of the current LDLt,. I have to check again, but if so, then
there is no reason not to keep the current LDLt version which could be
replaced by a more complex one with full pivoting.
On Wed, Jan 28, 2009 at 12:43 AM, Keir Mierle <mierle@xxxxxxxxx> wrote:
> Probably it's better to do full pivoting. Apparently cholesky is
> stable for semidefinite matrices when full pivoting is used:
>
> http://eprints.ma.man.ac.uk/1101/01/covered/MIMS_ep2008_56.pdf
>
> Keir
>
> On Tue, Jan 27, 2009 at 3:05 PM, Gael Guennebaud
> <gael.guennebaud@xxxxxxxxx> wrote:
>> Hi,
>>
>> yes, it seems the test to check whether the matrix is positive
>> definite was too strict. I changed the absolute tolerance a bit, but
>> we still need something better. Basically, in Cholesky we compute at
>> each iteration 1/sqrt(x), and so x must be >0 with some epsilon...
>>
>> Gael.
>>
>> On Tue, Jan 27, 2009 at 7:35 PM, Keir Mierle <mierle@xxxxxxxxx> wrote:
>>> Here is a testcase that fails with LLT and LDLT but works fine with
>>> all of LU, SVD, and QR solving. Depends on my previous patch for QR
>>> solver (or comment out the qr().solve line).
>>>
>>> Keir
>>>
>>
>>
>>
>
>
>