Timeline for Determinant of discrete Laplacian
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2016 at 9:00 | vote | accept | Matthias Ludewig | ||
| Jan 19, 2016 at 15:01 | answer | added | Gjergji Zaimi | timeline score: 3 | |
| Jan 19, 2016 at 12:43 | history | edited | Matthias Ludewig | CC BY-SA 3.0 |
added 206 characters in body
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| Jan 19, 2016 at 9:39 | comment | added | leo monsaingeon | By user35593's comment (which I didn't check but looks reasonable to me) you have lower and upper bounds on $ |det|$ in terms of what you expect, as soon as your partition is "approximately equidistant" $0<C_1\leq \frac{\Delta_i}{\Delta_j}\leq C_2$. However the scalings are different in the OP's 2 matrices: in order to stay consistent the first matrix should be multiplied by the uniform mesh $\Delta$, otherwise it doesn't make sense. Also, these matrices are the discretization of the positive operator "negative laplacian", not of the laplacian. | |
| Jan 19, 2016 at 9:15 | comment | added | user35593 | You can prove by induction that the determinant is $\prod_{i=1}^N \Delta_i \sum_{i=1}^N \frac{1}{\Delta_i}$ | |
| Jan 19, 2016 at 8:47 | history | asked | Matthias Ludewig | CC BY-SA 3.0 |