Timeline for Numerically computing the eigenvalues of an infinite-dimensional tridiagonal matrix
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2019 at 21:00 | history | tweeted | twitter.com/StackMma/status/1088904490378510337 | ||
| Jan 25, 2019 at 17:00 | vote | accept | user1620696 | ||
| Jan 25, 2019 at 15:12 | comment | added | Roman | Maybe I'll comment here that such matrices are specific to quantum mechanics and have properties that guarantee that in a low-energy subspace (i.e., a finite cutoff $n\le n_{\text{max}}$) the results are fairly accurate; there is no need for really taking $n$ to infinity. This can be motivated with arguments from physics. In a purely mathematical context, however, my recommendations and the code below would be insufficient in general. | |
| Jan 25, 2019 at 14:18 | comment | added | user1620696 | The matrices are the ones generated by @Roman's code. | |
| Jan 24, 2019 at 18:34 | comment | added | MikeY | Not familiar with the notation...are your matrices Toeplitz? Or does Roman's code generate the correct matrices? | |
| Jan 24, 2019 at 18:07 | answer | added | Roman | timeline score: 7 | |
| Jan 24, 2019 at 16:44 | comment | added | Roman | Have you tried summing only to a finite $n_{\text{max}}$ and seeing how the numerical eigenvalues converge as this upper limit increases? | |
| Jan 24, 2019 at 16:22 | comment | added | Daniel Lichtblau | What are these matrix components in Mathematica code? (I'm not asking for infinite dimensional vectors, just a clear indication of how one might form a finite upper left submatrix). | |
| Jan 24, 2019 at 16:15 | history | asked | user1620696 | CC BY-SA 4.0 |