000145467 001__ 145467 000145467 005__ 20250923084439.0 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$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000145467 590__ $$a3.3$$b2024 000145467 592__ $$a1.348$$b2024 000145467 591__ $$aMATHEMATICS, APPLIED$$b12 / 343 = 0.035$$c2024$$dQ1$$eT1 000145467 593__ $$aApplied Mathematics$$c2024$$dQ1 000145467 593__ $$aEngineering (miscellaneous)$$c2024$$dQ1 000145467 593__ $$aComputational Mathematics$$c2024$$dQ1 000145467 593__ $$aTheoretical Computer Science$$c2024$$dQ1 000145467 593__ $$aNumerical Analysis$$c2024$$dQ1 000145467 593__ $$aSoftware$$c2024$$dQ1 000145467 593__ $$aComputational Theory and Mathematics$$c2024$$dQ1 000145467 655_4 $$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__ $$a2025-09-22-14:49:34 000145467 980__ $$aARTICLE