000165841 001__ 165841 000165841 005__ 20260115140311.0 000165841 0247_ $$2doi$$a10.1007/s00211-020-01135-x 000165841 0248_ $$2sideral$$a118808 000165841 037__ $$aART-2020-118808 000165841 041__ $$aeng 000165841 100__ $$0(orcid)0000-0003-2156-9856$$aDelgado, J.$$uUniversidad de Zaragoza 000165841 245__ $$aExtremal and optimal properties of B-bases collocation matrices 000165841 260__ $$c2020 000165841 5060_ $$aAccess copy available to the general public$$fUnrestricted 000165841 5203_ $$aTotally 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. 000165841 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000165841 590__ $$a2.223$$b2020 000165841 591__ $$aMATHEMATICS, APPLIED$$b59 / 265 = 0.223$$c2020$$dQ1$$eT1 000165841 592__ $$a2.214$$b2020 000165841 593__ $$aComputational Mathematics$$c2020$$dQ1 000165841 593__ $$aApplied Mathematics$$c2020$$dQ1 000165841 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000165841 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, J.M.$$uUniversidad de Zaragoza 000165841 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000165841 773__ $$g146 (2020), 105-118$$pNumer. Math.$$tNUMERISCHE MATHEMATIK$$x0029-599X 000165841 8564_ $$s153784$$uhttps://zaguan.unizar.es/record/165841/files/texto_completo.pdf$$yPostprint 000165841 8564_ $$s1900344$$uhttps://zaguan.unizar.es/record/165841/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000165841 909CO $$ooai:zaguan.unizar.es:165841$$particulos$$pdriver 000165841 951__ $$a2026-01-15-12:36:27 000165841 980__ $$aARTICLE