Timeline for Fill-reducing ordering for computing the matrix product $A^T A$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 1 at 9:02 | comment | added | lightxbulb | Insofar as you use an iterative solver that requires products with $A^TA$ it does work. Are you by chance solving the normal equations $A^TAx=A^Tc$? If yes then look up CGNR/CGLS/LSQR. If not then you can maybe still use those, you just need to modify the first step to not apply the $A^T$ to $b$. Or you can use just the conjugate gradient solver with the matrix-vector multiplication as described. | |
| Mar 1 at 7:28 | comment | added | Ma Joad | @lightxbulb Thank you for the suggestion. But I want to SOLVE linear system of the form $A^TAx = b.$ Does your method here work? | |
| Mar 1 at 1:39 | answer | added | Abdullah Ali Sivas | timeline score: 5 | |
| Feb 29 at 22:17 | comment | added | lightxbulb | If $A$ is sparse could you not instead implement the matrix vector product with $A^TA$ through $y=Ax$ and $z=A^Ty$ and then $z=A^TAx$ as desired? As long as you're using iterative methods you can use this. Looking for a sparsity promoting fill-reducing ordering sounds like a much harder and computationally more expensive problem. | |
| Feb 29 at 22:10 | history | asked | Ma Joad | CC BY-SA 4.0 |