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A Practical Method for Floating-Point Gröbner Basis Computation

In: Computer Mathematics

Author

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  • Tateaki Sasaki

    (University of Tsukuba, Institute of Mathematics)

Abstract

Computing Gröbner bases with inexact coefficients is eagerly desired in industrial applications, but the computation with floating-point numbers is quite unstable if performed naively. In previous papers, the present author clarified that large term-cancellations occur frequently making the computation unstable, and he proposed a method of removing the harm of exact term-cancellations and a method of estimating the amounts of inexact term-cancellations. However, the estimation is very rough and never satisfactory. The inexact cancellations cause the accuracy loss of the output system, hence it is important to estimate their amounts precisely. In this chapter, we propose a practical method of estimating the amounts of inexact cancellations fairly well and very simply. We have tested our method by several examples, and obtained reasonable results. We also propose a simple device to reduce the amounts of exact term-cancellations.

Suggested Citation

  • Tateaki Sasaki, 2014. "A Practical Method for Floating-Point Gröbner Basis Computation," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 109-124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_10
    DOI: 10.1007/978-3-662-43799-5_10
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