Timeline for efficient way to compute the inversion of the following matrix
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2013 at 16:52 | answer | added | Michael | timeline score: 0 | |
| Aug 23, 2013 at 15:21 | answer | added | karakfa | timeline score: 0 | |
| Mar 21, 2011 at 15:06 | comment | added | Charles Staats | Have you thought of asking this question on StackOverflow? They might be a better resource if you are interested in practical computation. | |
| Mar 21, 2011 at 14:09 | answer | added | Brian Borchers | timeline score: 6 | |
| Mar 21, 2011 at 14:03 | answer | added | Aaron Meyerowitz | timeline score: 1 | |
| Mar 21, 2011 at 12:53 | comment | added | Steve Huntsman | mathoverflow.net/questions/8863/… | |
| Mar 21, 2011 at 9:30 | comment | added | Nancy | Yeah, you can alteratively think of this problem as solve a linear equation in terms of $Y$ such that $(E-aX)Y=E$. | |
| Mar 21, 2011 at 6:52 | comment | added | Gerry Myerson | @Nancy, I think what Thierry is saying is that what's efficient in theory may not be efficient in practice, and vice versa. Also, what's efficient when $n=10$ may not be when $n=10,000$, and also the answer may depend on just how sparse is sparse. | |
| Mar 21, 2011 at 6:50 | comment | added | Henry Cohn | There's also the question of whether you really want the inverse matrix. (For example, if you are trying to solve a system of linear equations, then computing the inverse is not the best approach.) The matrix $E-aX$ is diagonally dominant, which is an important hypothesis for analyzing iterative algorithms, such as the Jacobi method for solving systems of equations. | |
| Mar 21, 2011 at 6:47 | comment | added | Nancy | I am just wondering whether there would be some effciient way to optimize the ${E-a \cdot X}^{-1}$ computation? | |
| Mar 21, 2011 at 6:40 | history | edited | Nancy | CC BY-SA 2.5 |
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| Mar 21, 2011 at 6:21 | comment | added | Thierry Zell | What are you looking for? Good theoretical complexity or fast answer in practice? These are two different questions. | |
| Mar 21, 2011 at 6:04 | history | edited | S. Carnahan♦ | CC BY-SA 2.5 |
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| Mar 21, 2011 at 5:56 | history | asked | Nancy | CC BY-SA 2.5 |