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From: bimandre@saturnus.cs.kuleuven.ac.be (Andre Marien)
Newsgroups: sci.math,sci.math.num-analysis,comp.arch,comp.software-eng,comp.lang.prolog,comp.lang.misc,eunet.misc
Subject: Bignums, Rationals, Incremental gaussian elimination & simplex
Message-ID: <1722@n-kulcs.cs.kuleuven.ac.be>
Date: 4 Feb 91 14:34:33 GMT
Sender: news@cs.kuleuven.ac.be
Followup-To: sci.math.num-analysis
Organization: BIM, Everberg Belgium
Lines: 42
Originator: bimandre@saturnus

Hello,

I am looking for information on the following topics, and I do not
really know to which newsgroup to limit this message, I send it to a
few of them:

- Infinite Precision Arithmetic (i.e. bignums, rationals and others):
   * Bibliographic references (I am looking for something more recent
     and/or advanced that the volume 2 of D. Knuth book "Seminumerical
     Algorithms" which already contains a great deal of basic material
     on the subject).
   * Packages (any information on existing routines, their
     availability (cost, where, etc.), experience with them would be
     welcome).
   * Hardware assistance (Co-processors specialised to support
     infinite precision arithmetic).

- Algorithms to solve sets of linear equations (=) and inequations (<,
  <=, >, >=) in an INCREMENTAL way.

  The basic stuff for that is obviously gaussian elimination and the
  simplex algorithm but I am faced with the additional constraint that
  the resolution procedure must be incremental, i.e. equations and/or
  inequations can be added AND removed easily. I am looking for
  procedure(s) to check that a set of equations/inequations remains
  solvable (i.e. the set of solutions remains non-empty) whenever a
  new equation or inequation is added to a solvable set.

  The critical point is that adding/removing equations/inequations
  should involve as little overhead as possible.

  Any clue, bibliographic reference ?

Thanks in advance for any help.

Pierre-Joseph GAILLY		E-Mail: pjg@sunbim.be
B.I.M.-Zaventem			Phone : + 32 2 759 59 25 (Bim general)
Leuvensesteeweg 510,		      : + 32 2 719 26 11 (Bim Zaventem)
B-1930 Zaventem			Fax   : + 32 2 725 47 83
Belgique / Belgium