MathGroup Archive 1992

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  • To: mathgroup at
  • Subject: determinants
  • From: fateman at (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
Tateaki Sasaki and Hirokazu Mura,
Efficient Gaussian Elimination method for symbolic determinants
and linear systems
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. 


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