Timeline for Solving huge dense square symmetric linear system
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Feb 28, 2022 at 10:24 | comment | added | pinpon | @VictorEijkhout Huge GNSS network adjustment | |
| Feb 23, 2022 at 4:02 | comment | added | Victor Eijkhout | What is your science application? | |
| Jan 24, 2022 at 1:24 | comment | added | coolguy1000000 | Why not use an iterative solver? You have an SPD matrix, conjugate gradient method should do the trick if your matrix is reasonably conditioned. | |
| Jan 20, 2022 at 22:52 | history | edited | Maxim Umansky | CC BY-SA 4.0 |
fixed typo
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| Jan 20, 2022 at 12:52 | comment | added | pinpon | @IanBush I can also think of systems whose sparseness increase with the size of the problem. However, I can also think of systems that are not sparse at all and might not be easily approximated by a sparse system. | |
| Jan 20, 2022 at 12:50 | comment | added | pinpon | @FedericoPoloni I have edited the question to be more clear. | |
| Jan 20, 2022 at 12:48 | history | edited | pinpon | CC BY-SA 4.0 |
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| Jan 20, 2022 at 12:34 | comment | added | Federico Poloni | @BrianBorchers You're missing a division by 2 because $A$ is symmetric (but that doesn't change the conclusion). | |
| Jan 20, 2022 at 10:38 | comment | added | Ian Bush | @pinpon I also can think of many systems that are most easily and efficiently expressed as dense matrices at small size, but as the size increases they become increasingly sparse - and as such I would spend some time checking that a dense solver really is the most appropriate in this case. This is what I think is Wolfgang's point, and also part of my hesitation in giving an answer. | |
| Jan 20, 2022 at 9:18 | comment | added | pinpon | @IanBush Thanks! ScaLAPACK seems a good start! | |
| Jan 20, 2022 at 9:10 | comment | added | pinpon | @WolfgangBangerth why questionable? I can think of numerous problems that are really best described by a dense matrix. | |
| Jan 19, 2022 at 21:20 | comment | added | Wolfgang Bangerth | But even if possible, it seems questionable whether whatever you are doing is really best described by a dense matrix! | |
| Jan 19, 2022 at 15:28 | comment | added | Brian Borchers | You're going to need a system with a lot of memory to even store the matrix A. Multiply 500000 by 500000 by 8 bytes per entry and you'll have 2000 gigabytes of storage required for A. This isn't something you can do on a desktop machine, but could well be within the capacity of a high performance computing cluster. | |
| Jan 19, 2022 at 14:05 | comment | added | Ian Bush | Well I can tell you it is doable - on 16384 cores of a modern cluster a collaborator and I have demonstrated finding all evals and evecs of a dense, real, symmetric matrix of about that size which is a somewhat tougher calculation than you need. We used ScaLAPACK which also has solvers in, being the distributed memory version of LAPACK. So it is possible, but whether ScaLAPACK is a good way to go for your problem I feel less sure - hence a comment rather than an answer (basically I do diagonlisation, I rarely solve equations) | |
| Jan 19, 2022 at 9:30 | history | edited | pinpon | CC BY-SA 4.0 |
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| Jan 19, 2022 at 9:15 | history | asked | pinpon | CC BY-SA 4.0 |