Timeline for Ways to convert a Positive Semi-Definite (PSD) matrix -> Positive Definite matrix
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2012 at 20:53 | vote | accept | Alex | ||
| Apr 20, 2012 at 16:55 | comment | added | Alex | M is guaranteed to be a positive semi-definite (PSD) matrix. There is no guarantee that all eigenvalues are positive. Then, there is a potential problem with my paper because of my careless during the formulation (dmml.asu.edu/users/xufei/Papers/ICDM2011.pdf page 3). So I want to find a ``good'' solution in terms of stability for this matrix inversion problem. | |
| Apr 19, 2012 at 14:00 | answer | added | Brian Borchers | timeline score: 4 | |
| Apr 19, 2012 at 5:08 | comment | added | Brian Borchers | What do you know about $M$? In particular do you know whether it is simply rank deficient or whether it might be ill conditioned? In terms of the eigenvalues of $M$ are the nonzero eigenvalues well separated from the 0 eigenvalues, or could you have small nonzero eigenvalues? | |
| Apr 18, 2012 at 22:53 | comment | added | Alex | I mean stability. Will these two approaches differ significantly. My application uses the inverse matrix of the PSD matrix to solve the minimization problem, $\min ~ \| M^{1/2} L - M^{-1/2} N \|_F^{2} $ Here matrices M and N are known, and L is to be computed. I minimize the Frobenious norm, which can be solved by a set of least square problems. So different inverse matrices would affect the final solution of L. I would like to see any references discussing the effect of different transformation approaches (from PSD to PD). | |
| Apr 18, 2012 at 21:32 | comment | added | Federico Poloni | "better" for what purpose? The answer depends largely on that. Please add more detail. | |
| Apr 18, 2012 at 20:48 | history | asked | Alex | CC BY-SA 3.0 |