Timeline for Eigenvalues of a matrix constructed with simple logic
Current License: CC BY-SA 3.0
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Nov 26, 2013 at 1:53 | comment | added | Jake | The structure of this matrix might make it simpler to construct the matrix powers by logic manipulation (rather than standard sparse multiplication), so I could find a speedup with a customised iterative method. I'm wondering if this kind of structure could lead to a direct approach to Eigenvalue calculation by logical operations rather than numerical approaches - for a general matrix of this kind. More general models of similar problems are pretty solid (otherwise condensed matter would be much less... fun), but something about the simplicity of this structure is almost screaming out to me. | |
| Nov 26, 2013 at 1:39 | comment | added | Jake | I'm currently using LAPACK, though I will look into ARPACK (as it seems to be useful for large, sparse matrices - though I figured LAPACK would be good enough due to the pretty basic structure of the matrix). Thanks Federico for enlightening me about Arnoldi methods (and the Lanczos iteration which I was lead to from the WIKI page). | |
| Nov 25, 2013 at 23:11 | comment | added | Federico Poloni | Arpack is a specific software for that task; more in general the theoretical tool that you need is Arnoldi methods. The short answer is: yes, it is possible (at least approximately) to solve linear systems and compute some specific eigenvalues (such as the ones with largest or smallest modulus) relying only on a function that computes the matrix product $v \mapsto Mv$. | |
| Nov 25, 2013 at 21:10 | history | answered | guest | CC BY-SA 3.0 |