000128123 001__ 128123
000128123 005__ 20241125101129.0
000128123 0247_ $$2doi$$a10.1016/j.amc.2022.127611
000128123 0248_ $$2sideral$$a132373
000128123 037__ $$aART-2023-132373
000128123 041__ $$aeng
000128123 100__ $$aLi, Ch.
000128123 245__ $$aPACF: A precision-adjustable computational framework for solving singular values
000128123 260__ $$c2023
000128123 5060_ $$aAccess copy available to the general public$$fUnrestricted
000128123 5203_ $$aSingular value decomposition (SVD) plays a significant role in matrix analysis, and the differential quotient difference with shifts (DQDS) algorithm is an important technique for solving singular values of upper bidiagonal matrices. However, ill-conditioned matrices and large-scale matrices may cause inaccurate results or long computation times when solving singular values. At the same time, it is difficult for users to effectively find the desired solution according to their needs. In this paper, we design a precision-adjustable computational framework for solving singular values, named PACF. In our framework, the same solution algorithm contains three options: original mode, high-precision mode, and mixed-precision mode. The first algorithm is the original version of the algorithm. The second algorithm is a reliable numerical algorithm we designed using Error-free transformation (EFT) technology. The last algorithm is an efficient numerical algorithm we developed using the mixed-precision idea. Our PACF can add different solving algorithms for different types of matrices, which are universal and extensible. Users can choose different algorithms to solve singular values according to different needs. This paper implements the high-precision DQDS and mixed-precision DQDS algorithms and conducts extensive experiments on a supercomputing platform to demonstrate that our algorithm is reliable and efficient. Besides, we introduce the error analysis of the inner loop of the DQDS and HDQDS algorithms.
000128123 536__ $$9info:eu-repo/grantAgreement/ES/AEI/PID2021-122961NB-I00$$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R$$9info:eu-repo/grantAgreement/ES/MICINN/PGC2018-096026-B-I00
000128123 540__ $$9info:eu-repo/semantics/openAccess$$aby-nd$$uhttp://creativecommons.org/licenses/by-nd/3.0/es/
000128123 590__ $$a3.5$$b2023
000128123 592__ $$a1.026$$b2023
000128123 591__ $$aMATHEMATICS, APPLIED$$b10 / 332 = 0.03$$c2023$$dQ1$$eT1
000128123 593__ $$aComputational Mathematics$$c2023$$dQ1
000128123 593__ $$aApplied Mathematics$$c2023$$dQ1
000128123 594__ $$a7.9$$b2023
000128123 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000128123 700__ $$0(orcid)0000-0002-8089-343X$$aBarrio, R.$$uUniversidad de Zaragoza
000128123 700__ $$aXiao, X.
000128123 700__ $$aDu, P.
000128123 700__ $$aJiang, H.
000128123 700__ $$aQuan, Z.
000128123 700__ $$aLi, K.
000128123 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000128123 773__ $$g440 (2023), 127611 [20 pp.]$$pAppl. math. comput.$$tApplied Mathematics and Computation$$x0096-3003
000128123 8564_ $$s1037715$$uhttps://zaguan.unizar.es/record/128123/files/texto_completo.pdf$$yPostprint
000128123 8564_ $$s1516782$$uhttps://zaguan.unizar.es/record/128123/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000128123 909CO $$ooai:zaguan.unizar.es:128123$$particulos$$pdriver
000128123 951__ $$a2024-11-22-11:58:35
000128123 980__ $$aARTICLE