Timeline for Is there a fast matrix-free inverse power iteration?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 2, 2024 at 20:52 | comment | added | rchilton1980 | You might look into LOBPCG, I have had better luck with it than Lanczos/Arnoldi methods when it comes to finding small eigenpairs / inverse iteration. I would imagine it's not too hard to incorporate some shifting. | |
| Apr 14, 2024 at 3:37 | comment | added | Wolfgang Bangerth | ARPACK is an eigenvalue solver that does not require anything other than the action of a matrix. SLEPc can also handle matrices that are only provided via their action. | |
| Apr 13, 2024 at 21:07 | comment | added | Diplodokus | lightxbulb and @Laurent90 thank you for your comments, I'll try to apply the algorithms you suggested. Concerning the eigenvalues, all I can say (at least I think so....) is that 1 is the largest eigenvalue (Perron-Frobenius). Using $\mu=1$ would cause divergence. My concern is that using $\mu<1$ could cause the iteration to converge to another close eigenvalue/vector. Is this a valid concern? Moreover, I read that solving $(A-I)x=0$ could be difficult because methods tend to find the trivial solution $x=0$ (mathoverflow.net/questions/410566/…) | |
| Apr 13, 2024 at 19:47 | comment | added | Laurent90 | Maybe try solving $(A-I)x=0$ with a sparse direct solver (e.g MUMPS) or an iterative solver (e.g. GMRES). Maybe you will not need a preconditionner if the eigenvalues are all clustered, which might be the case here ? | |
| Apr 12, 2024 at 18:01 | comment | added | lightxbulb | For the inversion just solve problems of the form $(A-\mu I) y_{k+1} = y_k$ with some iterative solver. You can use some preconditioner for the iterative solver yes. You can also look into Arnoldi ir Lanczos iterations for the estimation of eigenvalues. | |
| S Apr 12, 2024 at 16:25 | review | First questions | |||
| Apr 17, 2024 at 13:24 | |||||
| S Apr 12, 2024 at 16:25 | history | asked | Diplodokus | CC BY-SA 4.0 |