Timeline for Exponential of large matrices
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 22, 2013 at 18:20 | comment | added | Terry Loring | A full diagonalization will not take advantage of sparsity. | |
| Sep 25, 2013 at 23:14 | history | edited | François G. Dorais | CC BY-SA 3.0 |
latex fixes
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| May 28, 2010 at 16:58 | comment | added | Mark Meckes | Xodarap says A is real symmetric, so it is indeed diagonalizable. So as Xodarap points out above, the real question is how to go about diagonalizing. | |
| May 28, 2010 at 16:33 | comment | added | Gunnar Þór Magnússon | You don't have to calculate all of the Taylor series. If you let P be the characteristic polynomial of the matrix, then you can write exp(A) = g(A) * P(A) + rest, where g is entire, and Cayley-Hamilton then gives exp(A) = rest (you can divide entire functions of matrices by polynomials). The rest can be calculated by finite differences, if I remember correctly. | |
| May 28, 2010 at 15:42 | comment | added | Xodarap | Do you know of a good way to diagonalize such a large matrix? Figuring out all 25k eigenvalues seems very time-consuming. | |
| May 28, 2010 at 15:20 | history | answered | John D. Cook | CC BY-SA 2.5 |