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MathGroup Archive 1992

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determinants

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: determinants
  • From: fateman at peoplesparc.berkeley.edu (Richard Fateman)
  • Date: Thu, 23 Apr 92 09:25:58 PDT

All the ideas (and then some) in Withoff's note on determinant
algorithms are, I think discussed in the papers below.

Sometimes what is an obvious and simple optimization, is dead wrong
in algorithms.  Some of these papers show such paradoxes..


J. Smit
A cancellation free algorithm, with factoring capabilities, for
the efficient solution of large sparse sets of equations,
Proc. 1981 ACM Symposium on  Symbolic and Algebraic Computation
(SYMSAC-81);
also
Tateaki Sasaki and Hirokazu Mura,
Efficient Gaussian Elimination method for symbolic determinants
and linear systems
(SYMSAC-81),
Sasaki and Y. Kanada,
Parallelism in algebraic computation and parallel algorithms for
symbolic linear systems,
also SYMSAC-81.
also see
Martin Griss, 
The algebraic solution of sparse linar systems via minor expansion, ACM Trans.
on Math Software, vol 2 1976 pp 31-49.

as well as the Gentleman-Johnson paper referred to earlier.

also, regarding my previous note: apologies for anthropomorphization.. 
 I suppose I should just say
Wolfram did not provide references to algorithms in his book (1st ed.)
on Mathematica.  He apparently refused to add references in his 2nd ed.

I appreciate Dave Withoff's willingness to accept questions (and
more --- provide answers) to technical questions. 

RJF







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