Timeline for How can we explicitly find the maximum eigenvalue of a tridiagonal matrix?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| May 28, 2010 at 13:34 | answer | added | alext87 | timeline score: 2 | |
| May 28, 2010 at 8:59 | comment | added | user6358 | Sorry, my question was a bit unclear. I hope it makes more sense now why I wrote -a_i/b_i,.etc I agree that it can be simplified according to TonyK. TonyK: My matrix is, in fact,(N+1)x(N+1). | |
| May 28, 2010 at 8:39 | history | edited | user6358 | CC BY-SA 2.5 |
added 181 characters in body
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| May 28, 2010 at 8:33 | history | rollback | user6358 |
Rollback to Revision 1
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| May 28, 2010 at 1:18 | answer | added | Wadim Zudilin | timeline score: 6 | |
| May 28, 2010 at 1:06 | comment | added | Jonas Meyer | Leandro: TonyK merely suggested making the problem notationally nicer. They are the same problem. (For instance, to explicitly get from the original version to the new formulation, take the special case where all denominators are -1.) @unknown (google): I'm also wondering whether the entries are real or complex. I hope you don't mind that I incorporated TonyK's suggestions. If you want, you can revert the edit. | |
| May 28, 2010 at 0:59 | history | edited | Jonas Meyer | CC BY-SA 2.5 |
simplified notation
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| May 27, 2010 at 23:59 | comment | added | Leandro | I think the problem who tonyK suggest is little bit more complicated. because the recursive relations are more general. In another direction, I would like to mention that a particular and interesting case of the above matrices occurs when it is symmetric. Probably you know, but if not, they are called Jacobi matrices and are related to Orthogonal polynomials and Riemann-Hilbert problems. The Percy Deift's book have a nice exposition about it. Orthogonal Polynomials and Random matrices: A Riemann-Hilbert approach | |
| May 27, 2010 at 23:23 | comment | added | TonyK | I think you got the penultimate entry in the rightmost column wrong. And probably the bottom row, too, unless your matrix is (N+1)x(N+1). But why bother with -a_i/b_i, -c_i/b_i etc at all? Why not just write a_i and c_i, and be done with it? It's the same problem. | |
| May 27, 2010 at 23:02 | history | asked | user6358 | CC BY-SA 2.5 |