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| Inverse of matrix square root http://forum.alglib.net/viewtopic.php?f=2&t=1564 |
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| Author: | remstadt [ Sun Mar 09, 2014 2:36 am ] |
| Post subject: | Inverse of matrix square root |
Hi, I was wondering which routine to use to get the fastest results with the least amount of computation... I have a symmetric 4x4 matrix, A, but there are two cases. (1) The matrix, A, is positive semi-definite i.e. may have a eigenvalue of 0. (2) The matrix, A, is positive definite. In either case I know ahead of time which type it is, so I can use the optimal routine when needed. I'm looking to solve for the matrix B, where B is defined as follows: B = P*D^(-1/2)*P^T where A = P*D*P^T, D is the diagonal matrix of eigenvalues of A. I will not need to know P or D after I obtain B. I would also like to know if there are refinements to this process in the case that A is a symmetric banded matrix, though this is less important. I'm considering using the VBA version of AlgLib, but if you were to point me to any of the routines in any language I can find the equivalent. |
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