多項式剰余列の安定な拡張算法

書誌事項

タイトル別名
  • A Stable Extended Algorithm for Generating Polynomial Remainder Sequence
  • 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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抄録

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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