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The authors thank the referee for his/her suggestions and comments which strongly improved earlierversions of this paper. We also thankj.M.R. Sanjurjo for his helpful comments. The first author was partially supported by DGES Grant MAT 2005-05730-CO2-02. The second author was partially supported by DGES grant MTM-2006-0825.

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Luzon, AnaAuthor

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Article

Riordan matrices in the reciprocation of quadratic polynomials

Publicated to:Linear Algebra And Its Applications. 430 (8-9): 2254-2270 - 2009-04-15 430(8-9), DOI: 10.1016/j.laa.2008.12.001

Authors: Luzon, Ana; Moron, Manuel A

Affiliations

Univ Complutense Madrid, Fac Matemat, Dept Geometria & Topol, E-28040 Madrid, Spain - Author
Univ Politecn Madrid, Dept Matemat Aplicada RR NN ETS Ingn Montes, E-28040 Madrid, Spain - Author

Abstract

We iterate contractive one-degree polynomials with coefficients in the ring K[vertical bar x vertical bar] of formal power series to calculate the reciprocal in K[vertical bar x vertical bar] of a quadratic polynomial. Doing this we meet thestructure of Riordan array. We interpret certain changes of variable as a Riordan array. We finish the paper by using our techniques to find new ways to get known formulas for the sum of powers of natural numbers involving Stirling and Eulerian numbers. (C) 2008 Elsevier Inc. All rights reserved.

Keywords

ArraysBanach's fixed point theoremChanges of variablesInverse relationsInvolutionsReciprocal of a quadratic polynomialRiordan matricesSums

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Linear Algebra And Its Applications due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2009, it was in position 65/202, thus managing to position itself as a Q2 (Segundo Cuartil), in the category Mathematics, Applied. Notably, the journal is positioned en el Cuartil Q2 para la agencia Scopus (SJR) en la categoría Numerical Analysis.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 4.03, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-11, the following number of citations:

  • WoS: 14
  • Scopus: 18
  • OpenCitations: 14

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-11:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 5 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (LUZON CORDERO, ANA MARIA) .