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I have to find the determinant of a symmetric square NxN matrix with M diagonals and M << N. Is there a more fast method than LU-decomposing the matrix?

TooTone
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Red
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  • Is it positive definite as well? – Harmen Apr 11 '14 at 09:42
  • @Harmen no, but it is real if this matters – Red Apr 11 '14 at 10:34
  • aren't row reductions to a lower (or upper) diagonal matrix going to be pretty efficient here as you can ignore all the zeros and do far fewer operations? – TooTone Apr 11 '14 at 11:42
  • @TooTone for a single calculation yes but I have to calculate a lot of such determinants. I am almost new to these arguments so I am only asking if the LU decomposition is the fastest way or if there exist faster methods – Red Apr 11 '14 at 11:49
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    @Red to be honest if it were me, I'd work through some examples and see if I could find a general formula. When I had to do something similar, I found [this](http://www.sosmath.com/matrix/determ1/determ1.html) useful. Finally as your question has no code, you might find it better to ask on math.se if there is a general formula, perhaps with a simple motivating example, and then come back here with some code. – TooTone Apr 11 '14 at 11:52

1 Answers1

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Yes, there are special methods for band(ed) matrices that solve elimination with O(N*M^2) complexity. Arbitrary found article of Jeff Thorson

MBo
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