doi:10.1080/03081087.2024.2304686engDelgado, JorgeOrera, HéctorPeña, J.M.High relative accuracy for rational q-Bernstein–Vandermonde matricesART-2024-137501In this article, an accurate and efficient method to compute the eigenvalues, singular values and inverses of nonsingular totally positive rational q-Bernstein–Vandermonde matrices and the solution of some associated linear systems of equations is provided. The method is based on the representation of a totally positive matrix in terms of its bidiagonal decomposition and the use of a library of accurate functions designed for this class of matrices. © 2024 Informa UK Limited, trading as Taylor & Francis Group.2024http://zaguan.unizar.es/record/13311110.1080/03081087.2024.2304686http://zaguan.unizar.es/record/133111oai:zaguan.unizar.es:133111info:eu-repo/grantAgreement/ES/DGA/E41-23Rinfo:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-TLinear and Multilinear Algebra 72, 17 (2024), 3052-3064by-nchttps://creativecommons.org/licenses/by-nc/4.0/deed.esinfo:eu-repo/semantics/openAccess