# Minimal numerical differentiation formulas

Minimal numerical differentiation formulas 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 $$\ell _1$$ ℓ 1 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerische Mathematik Springer Journals

# Minimal numerical differentiation formulas

, Volume 140 (3) – May 31, 2018
38 pages

/lp/springer_journal/minimal-numerical-differentiation-formulas-x9Og4YR0OX
Publisher
Springer Journals
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

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 $$\ell _1$$ ℓ 1 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.

### Journal

Numerische MathematikSpringer Journals

Published: May 31, 2018

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