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arXiv · 2310.13534

On Weighted Generalized Gauss Quadratures for M\"{u}ntz Systems

Huaijin Wang·Chuanju Xu
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Abstract

A novel recurrence formula for moments with respect to M\"{u}ntz-Legendre polynomials is proposed and applied to construct a numerical method for solving generalized Gauss quadratures with power function weight for M\"{u}ntz systems. These quadrature rules exhibit several properties similar to the classical Gaussian quadratures for polynomial systems, including positive weights, rapid convergence, and others. They are applicable to a wide range of functions, including smooth functions and functions with endpoint singularities, commonly found in integral equations with singular kernels, complex analysis, potential theory, and other areas.

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Huaijin Wang, Chuanju Xu. 2023-10-20. On Weighted Generalized Gauss Quadratures for M\"{u}ntz Systems. https://arxiv.org/abs/2310.13534

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