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Remarks on numerical integration, discrepancy, and diaphony

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arxiv 1711.07017 v1 pith:I4Y7KHKA submitted 2017-11-19 math.NA cs.NA

V.N. Temlyakov This is my paper · ORCID
classification math.NAcs.NA
keywords discrepancytheoryapproximationdevelopedintegrationnumericalboundsdiaphony
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The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work in proving lower bounds for recently developed new type of discrepancy -- the smooth discrepancy.

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  1. On the fixed volume discrepancy of the Fibonacci sets in the integral norms

    math.NA 2019-08 accept novelty 6.0 of 10

    For finite p, the periodic r-smooth fixed volume L_p discrepancy of the Fibonacci point set with b_n points is O(sqrt(log(b_n v)) / b_n^r); for p=∞ it is O(log(b_n v)/b_n^r).

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