000064490 001__ 64490 000064490 005__ 20190709135441.0 000064490 0247_ $$2doi$$a10.1016/j.amc.2017.01.031 000064490 0248_ $$2sideral$$a98119 000064490 037__ $$aART-2017-98119 000064490 041__ $$aeng 000064490 100__ $$0(orcid)0000-0003-2156-9856$$aDelgado, J.$$uUniversidad de Zaragoza 000064490 245__ $$aAccurate computations with Lupas matrices 000064490 260__ $$c2017 000064490 5060_ $$aAccess copy available to the general public$$fUnrestricted 000064490 5203_ $$aLupas q-analogues of the Bernstein functions play an important role in Approximation Theory and Computer Aided Geometric Design. Their collocation matrices are called Lupas matrices. In this paper, we provide algorithms for computing the bidiagonal decomposition of these matrices and their inverses to high relative accuracy. It is also shown that these algorithms can be used to perform to high relative accuracy several algebraic calculations with these matrices, such as the calculation of their inverses, their eigenvalues or their singular values. Numerical experiments are included. 000064490 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2015-65433-P 000064490 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000064490 590__ $$a2.3$$b2017 000064490 591__ $$aMATHEMATICS, APPLIED$$b21 / 252 = 0.083$$c2017$$dQ1$$eT1 000064490 592__ $$a1.065$$b2017 000064490 593__ $$aComputational Mathematics$$c2017$$dQ1 000064490 593__ $$aApplied Mathematics$$c2017$$dQ1 000064490 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000064490 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, J. M.$$uUniversidad de Zaragoza 000064490 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000064490 773__ $$g303 (2017), 171-177$$pAppl. math. comput.$$tApplied Mathematics and Computation$$x0096-3003 000064490 8564_ $$s102497$$uhttps://zaguan.unizar.es/record/64490/files/texto_completo.pdf$$yPreprint 000064490 8564_ $$s68895$$uhttps://zaguan.unizar.es/record/64490/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint 000064490 909CO $$ooai:zaguan.unizar.es:64490$$particulos$$pdriver 000064490 951__ $$a2019-07-09-11:36:18 000064490 980__ $$aARTICLE