Timeline for When is it easy to invert a sparse matrix?
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13 events
| when toggle format | what | by | license | comment | |
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| Jan 26, 2021 at 3:45 | answer | added | Reid.Atcheson | timeline score: 1 | |
| Sep 23, 2020 at 18:11 | history | edited | Yaroslav Bulatov |
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| Sep 23, 2020 at 18:06 | answer | added | Abdullah Ali Sivas | timeline score: 4 | |
| Sep 23, 2020 at 16:23 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
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| Sep 23, 2020 at 6:00 | history | tweeted | twitter.com/StackSciComp/status/1308647298193395712 | ||
| Sep 22, 2020 at 21:27 | comment | added | Wolfgang Bangerth | As a point in terminology, you're really looking at families of matrices with varying sizes. So a family of matrices all of which have have eigenvalues equal to just the elements of the same, small set (in other words, with a relatively small number of eigenvalues but growing multiplicities) can be solved in $O(N)$. That's because for all of the typical iterative methods, the number of iterations necessary is bounded by the number of distinct eigenvalues. | |
| Sep 22, 2020 at 20:49 | comment | added | Yaroslav Bulatov | by "fast" I mean that linear solver runtime is linear in the number of rows, while matrix inverse runtime is quadratic | |
| Sep 22, 2020 at 20:39 | comment | added | Yaroslav Bulatov | Either one -- since you can find inverse by solving k linear systems, having a fast linear solver will also give a fast inversion routine, and vica versa | |
| Sep 22, 2020 at 20:11 | comment | added | Federico Poloni | Are you using "invert" as in "solve a linear system with $A$" or as "compute the entries of the inverse of $A$"? | |
| Sep 22, 2020 at 19:23 | comment | added | Yaroslav Bulatov | Came across an interesting overview in Ch.1 rasmuskyng.com/rjkyng-dissertation.pdf, another easy case seems to be "symmetric M-matrix", case when $DMD$ is diagonally dominant for some diagonal $D$ | |
| Sep 22, 2020 at 18:50 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
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| Sep 22, 2020 at 18:24 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
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| Sep 22, 2020 at 18:18 | history | asked | Yaroslav Bulatov | CC BY-SA 4.0 |