Function Approximation, Numerical Differentiation and Numerical Indefinite Integration Based on Hyperfunction Theory

Abstract

Abstract. In this paper, we show a method of function approximation, numerical differentiation and numerical indefinite integration based on hyperfunction theory. In the proposed method, we obtain an approximation of a desired function by regarding it as a hyperfunction and computing approximately the standard defining function, which is an analytic function giving the desired function. Then, we obtain a numerical differentiation and a numerical indefinite integration by a simple procedure. Numerical examples show the effectiveness of the proposed method.