On Weighted Generalized Gauss Quadratures for M\"{u}ntz Systems
Numerical Analysis
2023-10-23 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2310.13534,
title = {On Weighted Generalized Gauss Quadratures for M\"{u}ntz Systems},
author = {Huaijin Wang and Chuanju Xu},
journal= {arXiv preprint arXiv:2310.13534},
year = {2023}
}