Timeline for Solve a large-scale linear system of equations with millions of unknowns
Current License: CC BY-SA 4.0
7 events
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| Feb 23, 2022 at 1:48 | comment | added | Neil Lindquist | Depends on the problem. CG can be useful if it converges fast enough to the desired precision. CG is bound by memory, and network performance w/ lots of synchronizations while Cholesky can get close to the peak arithmetic rate, so high iteration counts will make CG costly. Preconditioning is very helpful but requires tuning/knowledge of the problem. Cholesky is also useful for cases with multiple right hand sides. It's probably worth trying both if you going to be solving more than a couple systems, but people tend to look to Cholesky for dense problems. | |
| Feb 22, 2022 at 19:48 | comment | added | John Madden | Thanks for this interesting answer! I had always assumed that the largest scale linear systems were solved via some kinda krylov subspace method rather than just running a decomposition algorithm in parallel, but I guess methods like that, including CG, are best left to problems with specific structure which accelerates matvec computation? | |
| Feb 21, 2022 at 16:04 | comment | added | arc_lupus | Everything else would have been really interesting :-D. | |
| Feb 21, 2022 at 15:32 | comment | added | Neil Lindquist | That was a typo. It should be 16 GB. | |
| Feb 21, 2022 at 15:28 | history | edited | Neil Lindquist | CC BY-SA 4.0 |
Fixed typo in memory of V100 GPU
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| Feb 21, 2022 at 14:04 | comment | added | arc_lupus |
Just curious, is that a typo or real: 48 NVIDIA V100 GPUs (16 TB of memory each)? Or should it be 16 GB?
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| Feb 21, 2022 at 13:55 | history | answered | Neil Lindquist | CC BY-SA 4.0 |