Timeline for Matrix elements of exponential of tridiagonal matrices
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2018 at 20:10 | comment | added | Nawaf Bou-Rabee | In this context, I think a natural thing to do when $n$ is large is to use Monte Carlo instead of numerical linear algebra. Specifically compute the first passage times by simulating the underlying birth-death process associated to the tridiagonal $A$. Although one may need a large number of samples to resolve resulting the Monte Carlo error, typically this number is independent of $n$. | |
| S Feb 17, 2018 at 13:15 | history | suggested | Rodrigo de Azevedo | CC BY-SA 3.0 |
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| Feb 17, 2018 at 9:37 | review | Suggested edits | |||
| S Feb 17, 2018 at 13:15 | |||||
| Feb 17, 2018 at 8:58 | comment | added | Jochen Glueck | Do you wish to compute your matrix element for one time $t$ or for many times $t$? If the enormous computation time in your problem stems from a combination of $n$ being large and of evaluating $e^{tA}$ for many $t$'s, it could be very helpful to compute the diaganalisation of $A$ first (if it exists and is numerically stable - for this it would be helpful, of course, if $A$ was for instance symmetric). In this case, it would take some time to compute the diagonalisation at first, but afterwards you can compute your single matrix element of $e^{tA}$ with $\mathcal{O}(n)$ for each time $t$. | |
| Feb 17, 2018 at 8:50 | answer | added | Federico Poloni | timeline score: 12 | |
| Feb 17, 2018 at 1:35 | history | asked | stochastic | CC BY-SA 3.0 |