000125321 001__ 125321 000125321 005__ 20241125101153.0 000125321 0247_ $$2doi$$a10.1016/j.cam.2023.115064 000125321 0248_ $$2sideral$$a132946 000125321 037__ $$aART-2023-132946 000125321 041__ $$aeng 000125321 100__ $$0(orcid)0000-0003-2156-9856$$aDelgado, Jorge$$uUniversidad de Zaragoza 000125321 245__ $$aBidiagonal decompositions of Vandermonde-type matrices of arbitrary rank 000125321 260__ $$c2023 000125321 5060_ $$aAccess copy available to the general public$$fUnrestricted 000125321 5203_ $$aWe present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (-, -) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for nonsingular matrices to matrices of arbitrary rank. For totally nonnegative matrices of the above classes, the new decompositions can be computed efficiently and to high relative accuracy componentwise in floating point arithmetic. In turn, matrix computations (e.g., eigenvalue computation) can also be performed efficiently and to high relative accuracy. 000125321 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-17R$$9info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00 000125321 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000125321 590__ $$a2.1$$b2023 000125321 592__ $$a0.858$$b2023 000125321 591__ $$aMATHEMATICS, APPLIED$$b53 / 332 = 0.16$$c2023$$dQ1$$eT1 000125321 593__ $$aComputational Mathematics$$c2023$$dQ2 000125321 593__ $$aApplied Mathematics$$c2023$$dQ2 000125321 594__ $$a5.4$$b2023 000125321 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000125321 700__ $$aKoev, Plamen 000125321 700__ $$aMarco, Ana 000125321 700__ $$aMartínez, José-Javier 000125321 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, Juan Manuel$$uUniversidad de Zaragoza 000125321 700__ $$aPersson, Per-Olof 000125321 700__ $$aSpasov, Steven 000125321 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000125321 773__ $$g426 (2023), 115064 [15 pp.]$$pJ. comput. appl. math.$$tJournal of Computational and Applied Mathematics$$x0377-0427 000125321 8564_ $$s419431$$uhttps://zaguan.unizar.es/record/125321/files/texto_completo.pdf$$yVersión publicada 000125321 8564_ $$s1977142$$uhttps://zaguan.unizar.es/record/125321/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000125321 909CO $$ooai:zaguan.unizar.es:125321$$particulos$$pdriver 000125321 951__ $$a2024-11-22-12:08:00 000125321 980__ $$aARTICLE