000061590 001__ 61590
000061590 005__ 20190709135426.0
000061590 0247_ $$2doi$$a10.1016/j.laa.2016.12.003
000061590 0248_ $$2sideral$$a97529
000061590 037__ $$aART-2017-97529
000061590 041__ $$aeng
000061590 100__ $$aMarco, Ana
000061590 245__ $$aAccurate bidiagonal decomposition of totally positive Cauchy-Vandermonde matrices and applications
000061590 260__ $$c2017
000061590 5060_ $$aAccess copy available to the general public$$fUnrestricted
000061590 5203_ $$aCauchy–Vandermonde matrices play a fundamental role in rational interpolation theory and in other fields. When all their corresponding nodes are different and positive and all poles are different and negative and follow adequate orderings, these matrices are totally positive. In this paper we provide fast algorithms for computing bidiagonal factorizations of these matrices and their inverses with high relative accuracy. These algorithms can be used to solve with high relative accuracy other algebraic problems, such as the computation of all singular values, all eigenvalues or the solution of certain linear systems. The error analysis of the algorithm for computing the bidiagonal factorization and the corresponding perturbation theory are also performed.
000061590 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2015-65433-P
000061590 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000061590 590__ $$a0.972$$b2017
000061590 591__ $$aMATHEMATICS$$b76 / 309 = 0.246$$c2017$$dQ1$$eT1
000061590 591__ $$aMATHEMATICS, APPLIED$$b125 / 252 = 0.496$$c2017$$dQ2$$eT2
000061590 592__ $$a0.994$$b2017
000061590 593__ $$aAlgebra and Number Theory$$c2017$$dQ1
000061590 593__ $$aDiscrete Mathematics and Combinatorics$$c2017$$dQ1
000061590 593__ $$aGeometry and Topology$$c2017$$dQ2
000061590 593__ $$aNumerical Analysis$$c2017$$dQ2
000061590 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000061590 700__ $$aMartínez, José-Javier
000061590 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, Juan Manuel$$uUniversidad de Zaragoza
000061590 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000061590 773__ $$g517 (2017), 63-84$$pLinear algebra appl.$$tLINEAR ALGEBRA AND ITS APPLICATIONS$$x0024-3795
000061590 8564_ $$s389660$$uhttps://zaguan.unizar.es/record/61590/files/texto_completo.pdf$$yPreprint
000061590 8564_ $$s63192$$uhttps://zaguan.unizar.es/record/61590/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint
000061590 909CO $$ooai:zaguan.unizar.es:61590$$particulos$$pdriver
000061590 951__ $$a2019-07-09-11:29:15
000061590 980__ $$aARTICLE