Timeline for Automated decomposition of a large symbolic matrix for faster determinant calculation
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 25, 2022 at 16:43 | answer | added | user293787 | timeline score: 1 | |
| Oct 25, 2022 at 15:24 | comment | added | charmin | @user293787 Thanks. It does not look simpler; it is again $44$ dimensional matrix with four nonzero entries on each row. | |
| Oct 25, 2022 at 15:17 | comment | added | user293787 |
Define the two permutations p1={33,36,34,35,42,43,41,44,29,32,30,31,38,39,37,40,25,28,26,27,22,23,21,24,17,20,18,19,14,15,13,16,9,12,10,11,6,7,5,8,1,4,2,3} and p2={3,4,43,44,39,40,41,42,37,38,35,36,31,32,33,34,25,26,29,30,27,28,23,24,21,22,19,20,15,16,17,18,9,10,13,14,11,12,7,8,1,2,5,6}. Define X=M[[p1,p2]]. If you display X, you will see that it has a simpler structure than M (also try ListPlot[Map[First,ArrayRules[X]]]). Note that X and M have the same determinant, because p1 and p2 are even permutations. I do not know how to calculate the determinant of X however.
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| Oct 24, 2022 at 21:28 | comment | added | charmin | @Nasser Thank you very much for the explanation. | |
| Oct 24, 2022 at 19:37 | comment | added | Nasser | I am not sure it will make it faster if you change your one matrix, with multiplication of number of $m$ matrices instead and then find determinant of each of these and multiply the determinants. Since time to find the determinant is function of size of the matrix, and each one of the $m$ matrices has to be $n$ also, then this might actually be slower to do. But may be someone at math group knows more about this. As for the order, this is big O, it just says this is how you would expect the time to increase as a function of changing $n$. It does not give an actual time or anything like that. | |
| Oct 24, 2022 at 18:46 | history | edited | Syed | CC BY-SA 4.0 |
shortened title and removed one tag
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| Oct 24, 2022 at 18:09 | comment | added | charmin | @Nasser Thanks for your comments; as for your first comment then what is $\mathcal{O}(44^{2.372})$? As for the second comment, I thought maybe there is a Mathematica command for the decomposition of matrices. | |
| Oct 24, 2022 at 16:36 | comment | added | Nasser | Is it possible to decompose the matrix (as a multiplication of simpler matrices) so that computing its determinant is faster? I think this is now a math question so might be better ask at the math forum. | |
| Oct 24, 2022 at 16:33 | comment | added | Nasser | how much time it will take to give a result by Det[M] I think the best known algorithm is $O(n^{2.372...})$ where $n$ is the size of the matrix. | |
| Oct 24, 2022 at 16:05 | history | asked | charmin | CC BY-SA 4.0 |