Timeline for Ways to convert a Positive Semi-Definite (PSD) matrix -> Positive Definite matrix
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2012 at 2:17 | comment | added | Brian Borchers | Solving rank deficient and discrete ill-posed least squares problems is a very well studied subject. There's an inevitable tradeoff between stability of the computed solution with respect to round-off as well as error in the right hand side (your $N$ matrix) and biasing the solution away from a true least squares solution. By adjusting the regularization term, you can control in what direction the solution is biased by the regularization. By adjusting a regularization parameter you can control the trade-off between stability and bias. See for example Per Hansen's book. | |
| Apr 20, 2012 at 21:46 | comment | added | Alex | I am also interested in if there is any theoretical analysis to the stability of computing inverse ill-conditioned matrices. | |
| Apr 20, 2012 at 20:53 | vote | accept | Alex | ||
| Apr 20, 2012 at 17:06 | comment | added | Alex | Thanks Brian, very intuitive examples. The stability is exactly what I am concerned. The high level picture is that I want to solve a document clustering problem which can be finally converted to solve a set of least square problems. Then I get the potentially ill-conditioned matrix M. And now I need to find a good way to solve this problem. | |
| Apr 19, 2012 at 14:00 | history | answered | Brian Borchers | CC BY-SA 3.0 |