Comparison of Two Formulas for Approximating Functions with a Prescribed Decay Rate

Abstract

Abstract. For analytic functions characterized by weight functions expressing the decay properties of the functions, an interpolation type approximation formula has been devised by Sugihara, and it is known that optimal accuracy can be achieved with appropriate sampling points. In particular, when the weight decay exponentially, the best way to take sampling points is also known, and another formula has been devised by Ushima. In this paper, we extend Ushima's formula to the case when the weight function is general and perform error analysis. Numerical experiments showed that the extended Ushiima's formula was more accurate than Sugihara's formula in some cases.