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From: ckchiu@cs.cuhk.hk (CHIU Chong-kan)
Subject: Paper on Interval Constraint Solving ...
Message-ID: <Cyzr6G.Mu1@eng_ser1.erg.cuhk.hk>
Lines:  32
Sender: news@eng_ser1.erg.cuhk.hk
Organization: Engineering Faculty, The Chinese U. of Hong Kong
Date: Wed, 9 Nov 1994 08:20:39 GMT
Xref: glinda.oz.cs.cmu.edu comp.constraints:370 comp.lang.prolog:11644


The following paper is available by anonymous ftp from 
ftp.cs.cuhk.hk directory /pub/techreports/94, file 
seidel.ps.Z.

``Interval Linear Constraint Solving Using the Preconditioned 
  Interval Gauss-Seidel Method''

        C.K. Chiu and J.H.M. Lee ({ckchiu,jlee}@cs.cuhk.hk)
        Department of Computer Science
        The Chinese University of Hong Kong 
        Shatin, Hong Kong

We propose the use of the preconditioned interval Gauss-Seidel 
method as the backbone of an efficient linear equality solver 
in a CLP(Interval) language.  Since preconditioning involves 
multiplications between two matrices, a naive incorporation 
of the preconditioned interval Gauss-Seidel method in a CLP 
language incurs a time complexity of $O(n^4)$ in the worst 
case, where n is the number of variables in the linear system.  
In this paper, we give a novel incremental adaptation of the 
method of O(n^3) complexity.  The efficiency of the incremental
method is demonstrated using large-scale linear systems.  The 
incremental version also exhibits a near linear speed up over 
its non-incremental counterpart.


--
Chong-kan Chiu				Department of Computer Science
E-mail : ckchiu@cs.cuhk.hk 		The Chinese University of Hong Kong
Phone  : (852) 609-8403/4 		Shatin, Hong Kong
