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Fast Matrix Computation of Subresultant Polynomial Remainder Sequences

In: Computer Algebra in Scientific Computing

Author

Listed:
  • Alkiviadis G. Akritas

    (University of Thessaly
    University of Kansas)

  • Gennadi I. Malaschonok

    (Tambov University)

Abstract

We present an improved (faster) variant of the matrix-triangularization subresultant prs method for the computation of a greatest common divisor of two polynomials A and B (of degrees dA and dB, respectively) along with their polynomial remainder sequence [1]. The computing time of our fast method is 0(n2+ßlog ∥C∥2), for standard arithmetic and 0(((n1+ß+n 3 log ∥C∥)(log n+ log ∥C∥)2) for the Chinese remainder method, where n = d A + d B, ∥C∥ is the maximal coefficient of the two polynomials and the best known ß

Suggested Citation

  • Alkiviadis G. Akritas & Gennadi I. Malaschonok, 2000. "Fast Matrix Computation of Subresultant Polynomial Remainder Sequences," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing, pages 1-11, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57201-2_1
    DOI: 10.1007/978-3-642-57201-2_1
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