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cholinsert with sparse matrix

From: Daniel Kraft
Subject: cholinsert with sparse matrix
Date: Thu, 31 Jul 2014 09:10:08 +0200
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Is it possible to use cholinsert for sparse Cholesky factorisations?
When I try it out with some code like this:

A = rand (5, 5);
A = A' * A;
A = sparse (A);

R = chol (A);

As = A(1:4, 1:4);
Rs = chol (As);

RR = cholinsert (Rs, 5, A(:, 5));

RR is a dense matrix, while Rs is (as expected) sparse.  I don't really
know the implementation details of sparse Cholesky factorisations, so I
have no idea whether it is actually possible to do that -- but if it is,
this will help me a lot with my current code.

Also, in case it matters, my insert's will only ever be "extensions" and
not in the middle of the matrix (as in my example code above).  From my
understanding of the (ordinary, not sparse) Cholesky algorithm, this
corresponds to the situation of "halfway through" the algorithm, so it
should be easy to "continue" to factor the extended matrix.  Is there a
reason why this is not possible for sparse matrices, or is it simply
harder / not yet implemented?


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