Newsgroups: comp.lang.apl
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From: vpcsc4@sfsuvax1.sfsu.edu (Emmett McLean)
Subject: Re: Question: Tri-diagonal matrices in APL
Message-ID: <1993Apr29.233311.4264@csus.edu>
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Organization: San Francisco State University
References: <27APR93.10680596.0076@UNBVM1.CSD.UNB.CA> <1993Apr27.210112.2780@csus.edu> <1685@kepler1.rentec.com>
Date: Thu, 29 Apr 1993 23:33:11 GMT
Lines: 21

In article andrew@rentec.com (Andrew Mullhaupt) writes:
>>   NB.  multiplicative inverse of the tridiagonal?
>
>In practice, one should effectively NEVER compute this.
>tridiagonal matrix can be dense, but the triangular factors are also
>tridiagonal. The excess arithmetic in ignoring this important fact is
>catastrophic, and you will not get as accurate a solution, either. There
>being _no_ advantages to the inverse over the triangular factorization,
>one wonders where the interest lies.
>
>A quick glance through the bible (Golub and van Loan _Matrix Computations_)
>shows that pivoting can destroy the bandwidth of one of the factors, so
>you really hope not to have to do pivoting. The original poster gave a
>symmetric positive definite example, in which case pivoting is not needed. 
>
>
 I posted a program which calculates the inverse which does not use
 any pivoting at all. Andrew's comments about avoiding pivoting do not apply.

 Emmett

