Work

Totally Positive Wronskian Matrices and Symmetric Functions

Year: 2024

Type: article

Abstract: The elements of the bidiagonal decomposition (BD) of a totally positive (TP) collocation matrix can be expressed in terms of symmetric functions of the nodes. Making use of this result, and studying the relation between Wronskian and collocation matrices of a given TP basis of functions, we can express the entries of the BD of Wronskian matrices as the values of certain symmetric functions evaluated at a single node. Moreover, in the case of polynomial bases, we obtain compact formulae for the entries of the BD of their Wronskian matrices. Interesting examples illustrate the applications of the obtained formulae.

Source: Axioms

DOI: 10.3390/axioms13090589

Authors: Pablo Díaz, Esmeralda Mainar, Beatriz Rubio

Institutions: Universidad de Zaragoza, Instituto Universitario de Matemáticas y Aplicaciones

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funders: Gobierno de Aragón, Agencia Estatal de Investigación