安定化理論によるPadé近似計算について (数式処理とその周辺分野の研究)

Abstract

Padé approximation is a rational approximation constructed from the coefficients of a power series of a given function. The Padé approximation can be obtained by half GCD algorithm with complexity M(n)log n, where M(n) is polynomial multiplication cost, but the algorithm is unstable due to roundoff error if the input function has floating-point coefficients. In this paper, we show a stabilized half GCD algorithm to compute Padé approximation using the theory of stabilizing algebraic algorithms. We will show that the results have no Froissart doublets.