A Stable Extended Algorithm for Generating Polynomial Remainder Sequence

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  • OHSAKO Naoyuki
    Department of Information Engineering, School of Engineering Nagoya University
  • SUGIURA Hiroshi
    Department of Information Engineering, School of Engineering Nagoya University
  • TORII Tatsuo
    Department of Information Engineering, School of Engineering Nagoya University

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Other Title
  • 多項式剰余列の安定な拡張算法
  • タコウシキ ジョウヨレツ ノ アンテイ ナ カクチョウ サンポウ

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Abstract

Given two univariate polynomials F(z) and G(z), we show a stable extended algorithm for generating polynomial remainder sequence based on QR decomposition using Givens rotations. An arbitrary remainder polynomial P(z) of F(z) and G(z) can be written in the form P(z)=A(z)F(z)+B(z)G(z). Here, the each 2 norm of the pair (A(z), B(z)) is kept as constant one through all the Givens rotations, which guarantees the numerical stability of our method.

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