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