Timeline for solving series of linear systems with diagonal perturbations
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2010 at 10:55 | vote | accept | Fumiyo Eda | ||
| Aug 26, 2010 at 14:22 | comment | added | Pietro Majer | Yes, as I wrote. Nevertheless, finitely many expansions suffice to cover the set of {c}; whether this approach is efficient depends on the details. | |
| Aug 26, 2010 at 13:00 | comment | added | J. M. isn't a mathematician | Well, one can do it Krylov-style, assuming there is a nice black box for matrix-vector multiplications. Maintain a vector v initialized to the right-hand side, and at every iteration multiply this by E. But again, this is only feasible if it can be assured that the spectral radius of E/c never exceeds unity. | |
| Aug 26, 2010 at 12:50 | comment | added | Jiahao Chen | Is there a method to use the resolvent without computing it explicitly? It seems to use the resolvent would have to be recalculated for all cs, and explicit computation could result in massive fill-in (loss of sparsity) as @J. Mangaldan pointed out above once products like E^2 are computed. | |
| Aug 26, 2010 at 12:29 | comment | added | J. M. isn't a mathematician | Well, (E+cI)x=b can indeed be turned into something like (E/c+I)x=b/c, and thus you can use the geometric series technique. Of course, if the spectral radius of E/c is bigger than 1, this idea is shot. | |
| Aug 26, 2010 at 12:22 | history | answered | Pietro Majer | CC BY-SA 2.5 |