Cholesky update/downdate

Hi Douglas,

thanks for your answer.

My question indeed arises from a sparse matrix context: 'A' is sparse 
symmetric, and 'C' must also be sparse since it would otherwise fill.

It comes from a Bayes regression with a very large number of parameters; 
a loop over blocks will do the job in my specific case. Yet  I wondered 
about this since similar need for "covariance updating" may arise from 
linear filtering or kriging.

Douglas Bates wrote

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.