Minimal numerical differentiation formulas

Minimal numerical differentiation formulas Numerische Numer. Math. https://doi.org/10.1007/s00211-018-0973-3 Mathematik 1 2 Oleg Davydov · Robert Schaback Received: 12 December 2016 / Revised: 3 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We investigate numerical differentiation formulas on irregular centers in two or more variables that are exact for polynomials of a given order and minimize an absolute seminorm of the weight vector. Error bounds are given in terms of a growth function that carries the information about the geometry of the centers. Specific forms of weighted  and weighted least squares minimization are proposed that produce numerical differentiation formulas with particularly good performance in numerical experiments. The results are of interest in particular for meshless generalized finite difference methods as they provide a consistency error analysis for such methods. Mathematics Subject Classification 65D25 1 Introduction We consider a linear differential operator D of order k in d real variables in the notation |α| |α| ∂ ∂ α α Df = c ∂ f,∂ := = , |α|= α + ··· + α , (1) α 1 d α α 1 d ∂x ∂x ··· ∂x 1 d α∈Z |α|≤k Oleg Davydov oleg.davydov@math.uni-giessen.de Robert Schaback schaback@math.uni-goettingen.de Department of Mathematics, University http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerische Mathematik Springer Journals

Minimal numerical differentiation formulas

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Mathematical and Computational Engineering
ISSN
0029-599X
eISSN
0945-3245
D.O.I.
10.1007/s00211-018-0973-3
Publisher site
See Article on Publisher Site

Abstract

Numerische Numer. Math. https://doi.org/10.1007/s00211-018-0973-3 Mathematik 1 2 Oleg Davydov · Robert Schaback Received: 12 December 2016 / Revised: 3 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We investigate numerical differentiation formulas on irregular centers in two or more variables that are exact for polynomials of a given order and minimize an absolute seminorm of the weight vector. Error bounds are given in terms of a growth function that carries the information about the geometry of the centers. Specific forms of weighted  and weighted least squares minimization are proposed that produce numerical differentiation formulas with particularly good performance in numerical experiments. The results are of interest in particular for meshless generalized finite difference methods as they provide a consistency error analysis for such methods. Mathematics Subject Classification 65D25 1 Introduction We consider a linear differential operator D of order k in d real variables in the notation |α| |α| ∂ ∂ α α Df = c ∂ f,∂ := = , |α|= α + ··· + α , (1) α 1 d α α 1 d ∂x ∂x ··· ∂x 1 d α∈Z |α|≤k Oleg Davydov oleg.davydov@math.uni-giessen.de Robert Schaback schaback@math.uni-goettingen.de Department of Mathematics, University

Journal

Numerische MathematikSpringer Journals

Published: May 31, 2018

References

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