Distribution of Points in Convergent Sequences of Interpolatory Integration Rules: The Rates

Numerical Integration IV ◽

10.1007/978-3-0348-6338-4_3 ◽

1993 ◽

pp. 25-37

Author(s):

Tom Bloom ◽

Doron S. Lubinsky ◽

Herbert B. Stahl

Keyword(s):

Distribution Of Points ◽

Integration Rules ◽

Convergent Sequences

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Distribution of points for convergent interpolatory integration rules on (??, ?)

Constructive Approximation ◽

10.1007/bf01229336 ◽

1993 ◽

Vol 9 (1) ◽

pp. 59-82 ◽

Cited By ~ 1

Author(s):

T. Bloom ◽

D. S. Lubinsky ◽

H. Stahl

Keyword(s):

Distribution Of Points ◽

Integration Rules

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What distributions of points are possible for convergent sequences of interpolatory integration rules?

Constructive Approximation ◽

10.1007/bf01229335 ◽

1993 ◽

Vol 9 (1) ◽

pp. 41-58 ◽

Cited By ~ 5

Author(s):

T. Bloom ◽

D. S. Lubinsky ◽

H. Stahl

Keyword(s):

Integration Rules ◽

Convergent Sequences

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Maximally convergent sequences of multipoint Padé approximants and distribution of points of interpolation

10.1063/1.4854782 ◽

2013 ◽

Author(s):

Ralitza Kovacheva

Keyword(s):

Distribution Of Points ◽

Convergent Sequences

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Finite-order Integration Weights Can be Dangerous

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2007-0015 ◽

2007 ◽

Vol 7 (3) ◽

pp. 239-254 ◽

Cited By ~ 3

Author(s):

I.H. Sloan

Keyword(s):

Function Space ◽

Finite Order ◽

Small Subset ◽

Worst Case ◽

Integration Rule ◽

Dimensional Lattice ◽

3 Dimensional ◽

Sum Of Functions ◽

Integration Rules

Abstract Finite-order weights have been introduced in recent years to describe the often occurring situation that multivariate integrands can be approximated by a sum of functions each depending only on a small subset of the variables. The aim of this paper is to demonstrate the danger of relying on this structure when designing lattice integration rules, if the true integrand has components lying outside the assumed finiteorder function space. It does this by proving, for weights of order two, the existence of 3-dimensional lattice integration rules for which the worst case error is of order O(N¯½), where N is the number of points, yet for which there exists a smooth 3- dimensional integrand for which the integration rule does not converge.

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Some classes of ideal convergent sequences and generalized difference matrix operator

Filomat ◽

10.2298/fil1706827m ◽

2017 ◽

Vol 31 (6) ◽

pp. 1827-1834 ◽

Cited By ~ 14

Author(s):

S.A. Mohiuddine ◽

B. Hazarika

Keyword(s):

Matrix Operator ◽

Difference Matrix ◽

Convergent Sequences

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On the distribution of points of maximal deviation in complex Čebyšev approximation

Analysis Mathematica ◽

10.1007/bf01908217 ◽

1981 ◽

Vol 7 (4) ◽

pp. 257-263 ◽

Cited By ~ 1

Author(s):

A. Kroó

Keyword(s):

Distribution Of Points ◽

Maximal Deviation

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Distribution of points on Abelian covers over finite fields

International Journal of Number Theory ◽

10.1142/s1793042118500860 ◽

2018 ◽

Vol 14 (05) ◽

pp. 1375-1401 ◽

Cited By ~ 1

Author(s):

Patrick Meisner

Keyword(s):

Finite Fields ◽

Galois Extension ◽

Random Variables ◽

Families Of Curves ◽

Abelian Covers ◽

Distribution Of Points ◽

Genus Formula

We determine in this paper the distribution of the number of points on the covers of [Formula: see text] such that [Formula: see text] is a Galois extension and [Formula: see text] is abelian when [Formula: see text] is fixed and the genus, [Formula: see text], tends to infinity. This generalizes the work of Kurlberg and Rudnick and Bucur, David, Feigon and Lalin who considered different families of curves over [Formula: see text]. In all cases, the distribution is given by a sum of [Formula: see text] random variables.

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