ランダムな分布点での関数値に基づく一般化されたSimpson公式について

Abstract

The integration formulas of Newton-Cotes are given by the function-values at equally spaced abscissas. The Gaussian integration formulas are based on the values at nonequally spaced points distributed regularly by the orthogonal polynomials. On the other hand, it occurs often when we treat with the experimental data, that the calculation of integral must be done by using the values at random points in the interval. In this paper, we shall first establish the generalized Simpson's formula based on the data at irregularly distributed points. Next, we shall give the concrete form of the best formula having the highest order of accuracy in all the 3-points numerical integration formulas.