Re: [Rd] Cholesky update/downdate

From: Douglas Bates <bates_at_stat.wisc.edu>
Date: Thu, 29 Dec 2011 16:27:52 -0600

On Thu, Dec 29, 2011 at 8:05 AM, Yves Deville <deville.yves_at_alpestat.com> wrote:
> Dear R-devel members,

> I am looking for a fast Cholesky update/downdate. The matrix A being
> symmetric positive definite (n, n) and factorized as
> A = L %*% t(L), the goal is to factor the new matrix  A +- C %*% t(C) where
> C is (n, r). For instance, C is 1-column when adding/removing an observation
> in a linear regression. Of special interest is the case where A is sparse.

> Looking at the 'Matrix' package (help and source code), it seems that the
> CHOLMOD library shipped with 'Matrix' allows this,
> but is not (yet?) interfaced in 'Matrix', where the 'update' method for
> Cholesky decomposition objects seems limited to a new matrix A + m*I with a
> scalar (diagonal) modification.

The CHOLMOD library provides sparse matrix methods, especially the Cholesky decomposition and modifications to that decomposition, which is where the name comes from. Do you expect to work with sparse matrices?

I haven't seem too much code for update/downdate operations on the Cholesky decomposition for dense matrices. There were rank-1 update/downdate methods in Linpack but they didn't make it through to Lapack.
> If this is true: are there plans to implement such up/downdates?
>
> Best,
>
> Yves
>
> Yves Deville, statistical consultant, France.
>
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> R-devel@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel



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