165841 20260115140311.0 doi 10.1007/s00211-020-01135-x sideral 118808 ART-2020-118808 eng Delgado, J. Universidad de Zaragoza (orcid)0000-0003-2156-9856 Extremal and optimal properties of B-bases collocation matrices 2020 Totally positive matrices are related with the shape preserving representations of a space of functions. The normalized B-basis of the space has optimal shape preserving properties. Bernstein polynomials, B-splines and rational Bernstein bases are examples of normalized B-bases. It is proven that the minimal eigenvalue and singular value of a collocation matrix of a normalized B-basis is bounded below by the minimal eigenvalue and singular value of the corresponding collocation matrix of any normalized totally positive basis of the same space. The optimal conditioning for the 8-norm of a collocation matrix of a normalized B-basis among all the normalized totally positive bases of a space of functions is also shown. Numerical examples confirm the theoretical results and answer related questions. Access copy available to the general public Unrestricted info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 2.223 2020 MATHEMATICS, APPLIED 59 / 265 = 0.223 2020 Q1 T1 2.214 2020 Computational Mathematics 2020 Q1 Applied Mathematics 2020 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Peña, J.M. Universidad de Zaragoza (orcid)0000-0002-1340-0666 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 146 (2020), 105-118 Numer. Math. NUMERISCHE MATHEMATIK 0029-599X 153784 http://zaguan.unizar.es/record/165841/files/texto_completo.pdf Postprint 1900344 http://zaguan.unizar.es/record/165841/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:165841 articulos driver 2026-01-15-12:36:27 ARTICLE