171223 20260515163946.0 doi 10.1016/j.laa.2026.05.001 sideral 149309 ART-2026-149309 eng Khiar, Y. Universidad de Zaragoza (orcid)0000-0002-6497-7158 Accurate spectral computations and error analysis for r-geometric Min and Max matrices 2026 In this work, we introduce a new two-parameter family of structured matrices, termed r-geometric Min and Max matrices, which generalize both the r-Min/r-Max and geometric Min/Max matrices. We derive explicit bidiagonal factorizations for these matrices using Neville elimination and establish necessary and sufficient conditions under which they are totally positive. Under these conditions, we develop algorithms capable of computing their eigenvalues and singular values to high relative accuracy, as well as closed-form expressions for their determinants. We also apply perturbation theory to analyze the sensitivity of these problems to input data, deriving structured condition numbers that quantify the impact of data perturbations. Numerical experiments confirm the theoretical results and demonstrate the reliability and efficiency of the proposed algorithms across both the general r-geometric case and key special instances. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E41-23R 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 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 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 744 (2026), 131-152 Linear algebra appl. LINEAR ALGEBRA AND ITS APPLICATIONS 0024-3795 1005050 http://zaguan.unizar.es/record/171223/files/texto_completo.pdf Versión publicada 1403627 http://zaguan.unizar.es/record/171223/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:171223 articulos driver 2026-05-15-14:55:24 ARTICLE