Numerical integration of H "older continuous, absolutely convergent\n Fourier-, Fourier cosine-, and Walsh series

2013/12/04 by Josef Dick, Dick, Josef · 1 citation
Mathematics · Physics and Astronomy · #65C05 #65C10 #65D30 #65D32 #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.1312.1135

openalex publication_date 2013/12/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We introduce quasi-Monte Carlo rules for the numerical integration of\nfunctions f defined on [0,1]^s, s \≥ 1, which satisfy the following\nproperties: the Fourier-, Fourier cosine- or Walsh coefficients of f are\nabsolutely summable and f satisfies a H "older condition of order \α,\nfor some 0 < \α \≤ 1. We show a convergent rate of the integration error\nof order \max((s-1) N^-1/2, s^\α/2 N^-\α ). The construction of\nthe quadrature points is explicit and is based on Weil sums.\n

Citations

• Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients

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