000145467 001__ 145467
000145467 005__ 20241030091919.0
000145467 0247_ $$2doi$$a10.1007/s10915-024-02699-8
000145467 0248_ $$2sideral$$a140345
000145467 037__ $$aART-2024-140345
000145467 041__ $$aeng
000145467 100__ $$0(orcid)0000-0002-6497-7158$$aKhiar, Y.$$uUniversidad de Zaragoza
000145467 245__ $$aTotal Positivity and Accurate Computations Related to q-Abel Polynomials
000145467 260__ $$c2024
000145467 5060_ $$aAccess copy available to the general public$$fUnrestricted
000145467 5203_ $$aThe 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.
000145467 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/DGA/S60-23R$$9info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00$$9info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-T
000145467 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000145467 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000145467 700__ $$0(orcid)0000-0002-1101-6230$$aMainar, E.$$uUniversidad de Zaragoza
000145467 700__ $$0(orcid)0000-0003-1550-8168$$aRoyo-Amondarain, E.$$uUniversidad de Zaragoza
000145467 700__ $$0(orcid)0000-0001-9130-0794$$aRubio, B.$$uUniversidad de Zaragoza
000145467 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000145467 7102_ $$12006$$2200$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Didáctica Matemática
000145467 773__ $$g101 (2024), 1-22$$pJ. sci. comput.$$tJournal of Scientific Computing$$x0885-7474
000145467 8564_ $$s576252$$uhttps://zaguan.unizar.es/record/145467/files/texto_completo.pdf$$yVersión publicada
000145467 8564_ $$s1076416$$uhttps://zaguan.unizar.es/record/145467/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000145467 909CO $$ooai:zaguan.unizar.es:145467$$particulos$$pdriver
000145467 951__ $$a2024-10-30-08:49:03
000145467 980__ $$aARTICLE