Timeline for Is there a way to simplify block Cholesky decomposition if you already have decomposed the submatrices along the leading diagonal?
Current License: CC BY-SA 4.0
8 events
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| Mar 16, 2020 at 12:31 | history | edited | YCor | CC BY-SA 4.0 |
fixed bug in mathjax (bumping the question anyway)
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| Jul 8, 2010 at 18:10 | history | edited | Matthew Gretton | CC BY-SA 2.5 |
added 201 characters in body
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| Jul 8, 2010 at 0:31 | comment | added | Matthew Gretton | Yes. That's certainly true. Direct inversion of A^-1 is avoided in both cases... Q could potentially be low rank so as you say can't hurt to use the reformulation of Q. | |
| Jul 7, 2010 at 19:16 | comment | added | Jack Schmidt | Are you sure it helps with stability (in general)? You are still using A^-1/2 in your expression for Q. To compute BA^-1B, surely you would use the Cholesky decomposition of A to compute A^-1B (back solve), and so that already accounts for all the instability of A^-1: it occurs in both methods. Of course if Q is approximately low rank, then your factorization might help avoid some instability from the cancellation of C and BA^-1B, but I think that is separate. That said, your formula for Q cannot hurt, and has approximately the same operation count (n^2 more adds, but no big deal). | |
| Jul 7, 2010 at 18:08 | vote | accept | Matthew Gretton | ||
| Jul 9, 2010 at 0:57 | |||||
| Jul 7, 2010 at 18:07 | vote | accept | Matthew Gretton | ||
| Jul 7, 2010 at 18:08 | |||||
| Jul 7, 2010 at 18:07 | vote | accept | Matthew Gretton | ||
| Jul 7, 2010 at 18:07 | |||||
| Jul 7, 2010 at 18:04 | history | answered | Matthew Gretton | CC BY-SA 2.5 |