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Stable high order quadrature rules for scattered data and general weight functions. (English) Zbl 07236289

Summary: Numerical integration is encountered in all fields of numerical analysis and the engineering sciences. By now, various efficient and accurate quadrature rules are known, for instance, Gauss-type quadrature rules. In many applications, however, it might be impractical-if not even impossible-to obtain data to fit known quadrature rules. Often, experimental measurements are performed at equidistant or even scattered points in space or time. In this work, we propose stable high order quadrature rules for experimental data, which can accurately handle general weight functions.

MSC:

65D30 Numerical integration
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

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DLMF; OPQ
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References:

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