Timeline for Simultaneously orthogonally transform two SPD matrices to tridiagonal form?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 9, 2011 at 9:10 | comment | added | Suvrit | I think unless the matrices commute, in general you cannot simultaneously transform them this way. | |
| Aug 24, 2010 at 14:22 | answer | added | J. M. isn't a mathematician | timeline score: 4 | |
| Aug 24, 2010 at 14:03 | comment | added | J. M. isn't a mathematician | It's noteworthy to add that attempts to simplify the QZ algorithm (the standard method for the generalized eigenproblem) for symmetric definite pencils have all failed; this has something to do with the fact that the product of two symmetric matrices need not be symmetric. | |
| Aug 24, 2010 at 13:52 | history | edited | Greg | CC BY-SA 2.5 |
response to comment
|
| Aug 24, 2010 at 12:17 | comment | added | J. M. isn't a mathematician | For the benefit of search engines: this can also be referred to as the tridiagonalization of a symmetric-definite pencil. | |
| Aug 24, 2010 at 12:02 | comment | added | J. M. isn't a mathematician | Oh wow... as I recall this is one of the "Holy Grails" of numerical linear algebra; this is related to the search for much better algorithms for the "symmetric definite generalized eigenproblem", where the usual approach is to diagonalize one at the expense of making the other full (after which the usual methods for symmetric eigenproblems like QR are applied). This: maths.manchester.ac.uk/~ftisseur/reports/trd1.pdf is one result, but as Greg says, this isn't what he wants. | |
| Aug 24, 2010 at 9:50 | history | asked | Greg | CC BY-SA 2.5 |