複合多項式とその計算法

Abstract

Truncation of Fourier series causes Gibb's phenomenon, that is, undesirable oscillations occur near both ends and discontinuous points. To eliminate this, smoothing by Lanczos σ-factor is used. But, this method gives not so good results in many cases. It is well known that truncated Fourier series do not always converge uniformly to associated function. In this monograph, we present a new method to accelerate the convergence of Fourier series which converges slowly. This is composed of truncated Fourier series and some polynomials. Then we call this "composite polynomials". The computational methods of composite polynomial is also shown with FORTRAN subprograms.