Timeline for Whether should we consider the condition number of the preconditioned matrix when choosing a preconditioner?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 9, 2019 at 1:01 | vote | accept | Happy | ||
| Oct 17, 2019 at 15:18 | comment | added | Nick Alger | Try running GMRES on the upper triangular toeplitz matrix with 1's on the diagonal, 2's on the first superdiagonal, 3's on the second superdiagonal, and so on. The eigenvalues are all $1$, but the conditioning of the eigenvector matrix is horrendous so GMRES converges slowly. | |
| Oct 17, 2019 at 15:16 | comment | added | Amit Hochman | Note that if the eigenvalues cluster around zero, as happens for example when discretizing a smoothing operator, the condition number will be right in warning you that convergence will be slow. | |
| Oct 17, 2019 at 13:55 | answer | added | Reid.Atcheson | timeline score: 2 | |
| Oct 17, 2019 at 4:27 | history | edited | Happy | CC BY-SA 4.0 |
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| Oct 17, 2019 at 4:20 | history | asked | Happy | CC BY-SA 4.0 |