145467 20260217205559.0 doi 10.1007/s10915-024-02699-8 sideral 140345 ART-2024-140345 eng Khiar, Y. Universidad de Zaragoza (orcid)0000-0002-6497-7158 Total Positivity and Accurate Computations Related to q-Abel Polynomials 2024 Access copy available to the general public Unrestricted The attainment of accurate numerical solutions of ill-conditioned linear algebraic problems involving totally positive matrices has been gathering considerable attention among researchers over the last years. In parallel, the interest of q-calculus has been steadily growing in the literature. In this work the q-analogue of the Abel polynomial basis is studied. The total positivity of the matrix of change of basis between monomial and q-Abel bases is characterized, providing its bidiagonal factorization. Moreover, well-known high relative accuracy results of Vandermonde matrices corresponding to increasing positive nodes are extended to the decreasing negative case. This further allows to solve with high relative accuracy several algebraic problems concerning collocation, Wronskian and Gramian matrices of q-Abel polynomials. Finally, a series of numerical tests support the presented theoretical results and illustrate the goodness of the method where standard approaches fail to deliver accurate solutions. info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/DGA/S60-23R info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00 info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-T info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es 3.3 2024 MATHEMATICS, APPLIED 12 / 344 = 0.035 2024 Q1 T1 1.348 2024 Applied Mathematics 2024 Q1 Computational Mathematics 2024 Q1 Computational Theory and Mathematics 2024 Q1 Theoretical Computer Science 2024 Q1 Numerical Analysis 2024 Q1 Software 2024 Q1 Engineering (miscellaneous) 2024 Q1 4.8 2024 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Mainar, E. Universidad de Zaragoza (orcid)0000-0002-1101-6230 Royo-Amondarain, E. Universidad de Zaragoza (orcid)0000-0003-1550-8168 Rubio, B. Universidad de Zaragoza (orcid)0000-0001-9130-0794 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 2006 200 Universidad de Zaragoza Dpto. Matemáticas Área Didáctica Matemática 101 (2024), 1-22 J. sci. comput. Journal of Scientific Computing 0885-7474 576252 http://zaguan.unizar.es/record/145467/files/texto_completo.pdf Versión publicada 1076416 http://zaguan.unizar.es/record/145467/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:145467 articulos driver 2026-02-17-20:44:08 ARTICLE