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.
