ランダムデータに基づく数値積分とその最良形について

Abstract

When we deal with the experimental data, it occurs often that we must calculate the definite integral using the function-values at random finite points under the condition that not only the primitive function but also the integrand itself is unknown. The main aim of this study is to obtain the concrete form of numerical integration based on the function values at random points on the interval. And we shall determine the most accurate integration formula based on the values at no equally spaced two or three abscissas.