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Re: Efficient backsubstitution for upper triangular matrix

From: David Bateman
Subject: Re: Efficient backsubstitution for upper triangular matrix
Date: Fri, 26 Aug 2005 09:48:12 +0200
User-agent: Mozilla Thunderbird 0.8 (X11/20040923)

Paul Roberts wrote:


I was wondering if there is a explicit function in octave to
efficiently compute the solution to: Ax = b when A is upper triangluar
and non-singular.


This one is on my ToDo list. I've done a poly-morphic solver for the sparse matrices that includes special cases for the solves of triangular matrices, but it is definitely worthwhile to do the same thing for full triangular, positive definite and perhaps even permuted triangular matrices... You can use the matrix_type function in 2.9.3 to flag the matrix type or just let octave figure it out for itself, which is fairly efficient. So if your matrix is sparse then in 2.9.3 there are the tools you need to do this.

In octave-forge there is a cholesky function that is then combined with a home rolled back subsitution (not dtrsm unfortunately) and a special triangular matix type, but has no way to flag a matrix as triangular, so it is quite limited and not as fast as it could be since it does profit from ATLAS.

In any case I intend to have the special treatment of full triangular matries done for version 3.0.


David Bateman                                address@hidden
Motorola Labs - Paris +33 1 69 35 48 04 (Ph) Parc Les Algorithmes, Commune de St Aubin +33 1 69 35 77 01 (Fax) 91193 Gif-Sur-Yvette FRANCE

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