Mitch Schwartz

Realm of Existence

dansesacrale.wordpress.com

Age: 30

This is a great site; glad to be a part of it.

Jul
21
comment Find the maximum determinant for each size Toeplitz matrix
@RetoKoradi "So yes, assuming that the main diagonal is 1 would not work for very long." does not follow logically from "The best solution my code got for n=17 has 0 in the main diagonal. I did not check if there are tied solutions that have a 1 diagonal."
Jul
19
comment Find the maximum determinant for each size Toeplitz matrix
@RetoKoradi The max is sometimes reached with 0s in the main diagonal, e.g. for n=3 there is [0,1,1;1,0,1;1,1,0], and the next one occurs for n=6. I checked that for n=1..12 there is always at least one matrix with 1s in the main diagonal that reaches the max, but that's not the same as what you wrote.
Jul
19
comment Find the maximum determinant for each size Toeplitz matrix
@RetoKoradi Yes I saw that. It seems the complexity is not polynomial, considering that e.g. e_{k+1} has 4 times the number of components as e_k. There are many omissions in the paper. An invertible matrix has an LU decomposition iff all leading principal minors are nonzero. (Notice the denominators, e.g. a_0 -- implicitly they are guaranteed to be nonzero.) Uniqueness comes from L being unit triangular. The author also didn't mention numerical stability. In case the link becomes unavailable, the paper is "On Calculating the Determinants of Toeplitz Matrices" by Hsuan-Chu Li (2011).
Jul
19
answered Find the maximum determinant for each size Toeplitz matrix
Jun
26
revised Check if there is an isomorph substring
improvement
Jun
24
revised Check if there is an isomorph substring
improvement
Jun
23
revised Check if there is an isomorph substring
fix bug involving strings of length one
Jun
23
revised Check if there is an isomorph substring
improvement
Jun
23
revised Check if there is an isomorph substring
improvement
Jun
23
awarded Autobiographer
Jun
23
revised Check if there is an isomorph substring
improvement
Jun
23
revised Check if there is an isomorph substring
improvement
Jun
23
revised Check if there is an isomorph substring
improvement with complexity note
Jun
23
revised Check if there is an isomorph substring
improve algorithm description
Jun
23
comment Best place for learning GolfScript?
I don't think "Don't learn GolfScript" is a good answer for somebody expressing an interest to learn GolfScript.
Jun
22
answered Best place for learning GolfScript?
Jun
22
revised Check if there is an isomorph substring
improvement
Jun
22
revised Check if there is an isomorph substring
improvement
Jun
22
revised Check if there is an isomorph substring
improvement
Jun
22
awarded Commentator
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