Subject: Help with very very slow determinant calcuation
From: Bernard Hurley
Date: Sun, 07 Aug 2011 15:55:36 +0100
On Sun, 2011-08-07 at 05:18 -0500, Barton Willis wrote:
> The cost for the function determinant is comparable to the cost of a LU factorization. So, no
> computing the determinant by means of the LU factorization is unlikely to help. Nghia Ho already
> tried setting ratmx to true and newdet. And that's about all that might speed up the
> calculation.
>
> For symbolic matrices, the standard big oh time estimates are misleading. The time for addition,
> for example, isn't constant, but the time depends on the complexity of the expressions.
>
> It's likely that if Maxima was able to find the determinant of this 10x10 symbolic matrix, the
> result would be so huge that it wouldn't be useful. I would suggest a different approach.
>
An n x n determinant of terms of the form x[1,1],..., x[1,n],
x[2,1]...., x[n,n] is the sum of n! terms each the product of n terms.
There is no getting away from that however you evaluate the determinant!
Using elementary row/column operations on a matrix of numbers can be
used to reduce it to diagonal form and then evaluate the determinant of
that but this is of no help with pure symbols.
Cheers,
Bernard.