On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases-Reference-Cited by-同舟云学术

On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases

Published:2023-08-29 Issue:9 Volume:12 Page:839
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Mainar Esmeralda¹^ORCID,Peña Juan Manuel¹^ORCID,Rubio Beatriz¹^ORCID

Affiliation:

1. Department of Applied Mathematics, University Research Institute of Mathematics and Its Applications (IUMA), University of Zaragoza, 50009 Zaragoza, Spain

Abstract

A new class of matrices defined in terms of r-Stirling numbers is introduced. These r-Stirling matrices are totally positive and determine the linear transformation between monomial and r-Bell polynomial bases. An efficient algorithm for the computation to high relative accuracy of the bidiagonal factorization of r-Stirling matrices is provided and used to achieve computations to high relative accuracy for the resolution of relevant algebraic problems with collocation, Wronskian, and Gramian matrices of r-Bell bases. The numerical experimentation confirms the accuracy of the proposed procedure.

Funder

MCIU/AEI

Gobierno de Aragón

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/9/839/pdf

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5. Riordan, J. (1958). An Introduction to Combinatorial Analysis, Wiley.