抄録
From the viewpoint of numerical stability, Euclidean algorithm has still a problem even when we generate the univeriate polynomial remainder sequence. As we have to determine whether the remainder polynomial is zero or not to get the GCD(greatest common divisor)of two polynomials F(z)and G(z), it is difficult to distinguish the zero under the floating point arithmetic. In order to overcome this difficulty, we propose a stable algorithm to evaluate the subresultant by introducing pivoting in the process of elimination of leading coefficients of the polynomial. By our method, we can stably calculate a subsequence of polynomial remainder sequence.
