Timeline for Finding a similarities and differences of sent of matrices
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2018 at 11:49 | history | edited | User11441 | CC BY-SA 4.0 |
deleted 947 characters in body; edited title
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| Mar 23, 2018 at 13:52 | answer | added | Mark L. Stone | timeline score: 1 | |
| Mar 23, 2018 at 12:24 | comment | added | Mark L. Stone | Are covariance matrices complex, not real? If so, then MSE is complex not real, so doesn't make sense as an objective function. | |
| Mar 23, 2018 at 11:42 | comment | added | Mark L. Stone | I was suggesting using your existing approach to find a value of X which can be used as a starting value for a numerical nonlinear optimization. If there are extra requirements on the properties or structure of X beyond being an N by N REAL matrix which minimizes MSE, you need to say what they are. Are all matrices actually real, not complex? If so, why use $X^H$ rather than $X^T$? N=500 will be much harder to solve than X=50. Either use numerical differentiation or automatic differentiation (perhaps, ADiMat in order to handle matrix calculations) or Matrix Cookbook. | |
| Mar 23, 2018 at 1:29 | comment | added | Mark L. Stone | You could do numerical nonlinear optimization of MSE w.r.t. X, using your eignevector-based X as starting value. if that is fairly near to the optimum, it might not be too bad. If you "need to" get rid of the inverse, you can replace $(X^{H}R_{k}X+{I})^{-1}$ by $Y_k$ with $Y_k$ being another matrix variable for each k, and adding the constraints $Y_k(X^{H}R_{k}X+{I}) = I$. How large is N? | |
| Mar 22, 2018 at 15:25 | review | First posts | |||
| Mar 22, 2018 at 15:39 | |||||
| Mar 22, 2018 at 15:24 | history | asked | User11441 | CC BY-SA 3.0 |