Timeline for Verification in Eigenvalue problems
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2019 at 5:22 | answer | added | user20857 | timeline score: 3 | |
| Aug 22, 2017 at 22:32 | answer | added | user7440 | timeline score: 2 | |
| S Jun 16, 2016 at 16:29 | history | bounty ended | CommunityBot | ||
| S Jun 16, 2016 at 16:29 | history | notice removed | CommunityBot | ||
| Jun 8, 2016 at 20:20 | comment | added | nicoguaro♦ | @CarlChristian, yes I think that both would be useful. In general, one would like to determine that the method/software used presents the right order of convergence. That's why the Method of Manufactured Solutions is widely used. | |
| Jun 8, 2016 at 17:08 | comment | added | Carl Christian | I want to be sure that I have understood you correctly. Do you want to know how to estimate the distance between computed eigenpairs for discrete operator (matrix or matrices) and the corresponding eigenpair for the smooth operator? Or do you want to now how to estimate the accuracy by which you have solved a discrete eigenvalue problem? | |
| S Jun 8, 2016 at 15:27 | history | bounty started | Paul | ||
| S Jun 8, 2016 at 15:27 | history | notice added | Paul | Draw attention | |
| Aug 8, 2015 at 1:21 | history | edited | nicoguaro♦ | CC BY-SA 3.0 |
Fixing typo
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| Aug 8, 2015 at 1:21 | comment | added | nicoguaro♦ | @JesseChan, yes it seems so. But for some reason, Kirill answer does not look trivial/obvious to me. | |
| Aug 8, 2015 at 1:02 | comment | added | Jesse Chan | That's too bad. To be fair, I think Kirill's suggestion is probably far more useful than mine. | |
| Aug 8, 2015 at 0:45 | comment | added | nicoguaro♦ | @JesseChan, thanks for the suggested reading. It took me some time but I read it. I don't think that they provide enough information for the desired purpose. | |
| Jul 15, 2015 at 4:23 | comment | added | Kirill | In one dimension, if you start with desired $k,v$, and have $(\mathcal{L}+k^2)v = w \neq0$, you could try to decompose $w = fv+gv'$, if such $f,g$ exist, and then run with $\mathcal{L}'=\mathcal{L}-f-g\partial$. This can mess up $\mathcal{L}$'s symmetries and other properties, I suppose. Here $v$ and $v'$ should be linearly independent, and can't vanish at the same point. | |
| Jul 15, 2015 at 4:05 | comment | added | nicoguaro♦ | Yes, you can compare with analytic solutions. But normally they are provided for really simple cases. The question is about how to do the verification process. If there is something similar to the method oh manufactured solutions. Or if you should combine this method for other problems with analytical solutions. | |
| Jul 15, 2015 at 4:03 | comment | added | Jesse Chan | Can you compare your results to the spectra for known cases (square, cube, circle, sphere)? There are also expected convergence rates for eigenvectors and eigenvalues in appropriate norms that you can check (though these rates tend to vary depending on frequency - see journals.cambridge.org/action/…) | |
| Jul 15, 2015 at 1:44 | history | tweeted | twitter.com/#!/StackSciComp/status/621133179391475713 | ||
| Jul 15, 2015 at 1:29 | history | edited | nicoguaro♦ | CC BY-SA 3.0 |
added 116 characters in body
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| Jul 14, 2015 at 22:38 | history | edited | nicoguaro♦ | CC BY-SA 3.0 |
More precise option for alternative verification
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| Jul 14, 2015 at 22:27 | history | asked | nicoguaro♦ | CC BY-SA 3.0 |