Baglama, James; Perović, Vasilije; Toolan, Timothy Note on a rank-one modification of the singular value decomposition. (English) Zbl 07736201 Appl. Math. Comput. 457, Article ID 128170, 15 p. (2023). MSC: 65Fxx 15Axx 15-XX PDFBibTeX XMLCite \textit{J. Baglama} et al., Appl. Math. Comput. 457, Article ID 128170, 15 p. (2023; Zbl 07736201) Full Text: DOI
Ou, Xiaofeng; Xia, Jianlin SuperDC: superfast divide-and-conquer eigenvalue decomposition with improved stability for rank-structured matrices. (English) Zbl 1501.65019 SIAM J. Sci. Comput. 44, No. 5, A3041-A3066 (2022). MSC: 65F15 65F55 15A18 15A23 PDFBibTeX XMLCite \textit{X. Ou} and \textit{J. Xia}, SIAM J. Sci. Comput. 44, No. 5, A3041--A3066 (2022; Zbl 1501.65019) Full Text: DOI
Barlow, Jesse L.; Eisenstat, Stanley C.; Stor, Nevena Jakovčević; Slapnicar, Ivan Deflation for the symmetric arrowhead and diagonal-plus-rank-one eigenvalue problems. (English) Zbl 1492.65085 SIAM J. Matrix Anal. Appl. 43, No. 2, 681-709 (2022). MSC: 65F15 65G50 15-04 15B99 PDFBibTeX XMLCite \textit{J. L. Barlow} et al., SIAM J. Matrix Anal. Appl. 43, No. 2, 681--709 (2022; Zbl 1492.65085) Full Text: DOI
Wang, Hefeng; Xiang, Hua A quantum eigensolver for symmetric tridiagonal matrices. (English) Zbl 1417.81103 Quantum Inf. Process. 18, No. 3, Paper No. 93, 11 p. (2019). MSC: 81P68 15A18 68U20 68Q10 93C80 PDFBibTeX XMLCite \textit{H. Wang} and \textit{H. Xiang}, Quantum Inf. Process. 18, No. 3, Paper No. 93, 11 p. (2019; Zbl 1417.81103) Full Text: DOI
Bosch, Jessica; Greif, Chen Numerical solution of linear eigenvalue problems. (English) Zbl 1385.65029 Girouard, Alexandre (ed.) et al., Geometric and computational spectral theory. Lectures from the Séminaire de Mathématiques Supérieures, Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada, June 15–26, 2015. Providence, RI: American Mathematical Society (AMS); Montreal: Centre de Recherches Mathématiques (CRM) (ISBN 978-1-4704-2665-1/pbk; 978-1-4704-4258-3/ebook). Contemporary Mathematics 700. Centre de Recherches Mathématiques Proceedings, 117-153 (2017). MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{J. Bosch} and \textit{C. Greif}, Contemp. Math. 700, 117--153 (2017; Zbl 1385.65029) Full Text: DOI Link
Vogel, James; Xia, Jianlin; Cauley, Stephen; Balakrishnan, Venkataramanan Superfast divide-and-conquer method and perturbation analysis for structured eigenvalue solutions. (English) Zbl 1338.65104 SIAM J. Sci. Comput. 38, No. 3, A1358-A1382 (2016). MSC: 65F15 65F30 15A18 15A42 PDFBibTeX XMLCite \textit{J. Vogel} et al., SIAM J. Sci. Comput. 38, No. 3, A1358--A1382 (2016; Zbl 1338.65104) Full Text: DOI
Frederix, Katrijn; Delvaux, Steven; Van Barel, Marc An algorithm for computing the eigenvalues of block companion matrices. (English) Zbl 1260.65024 Numer. Algorithms 62, No. 2, 261-287 (2013). MSC: 65F15 15A54 PDFBibTeX XMLCite \textit{K. Frederix} et al., Numer. Algorithms 62, No. 2, 261--287 (2013; Zbl 1260.65024) Full Text: DOI Link
Benner, Peter; Embree, Mark; Lehoucq, Richard B.; Kelley, C. T. A mathematical biography of Danny C. Sorensen. (English) Zbl 1238.01104 Linear Algebra Appl. 436, No. 8, 2717-2724 (2012). MSC: 01A70 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 436, No. 8, 2717--2724 (2012; Zbl 1238.01104) Full Text: DOI
Boonyasiriwat, C.; Sikorski, K.; Tsay, C. Circumscribed ellipsoid algorithm for fixed-point problems. (English) Zbl 1220.65064 Math. Comput. 80, No. 275, 1703-1723 (2011). MSC: 65J15 47H10 47J25 47H09 65H10 65Y20 PDFBibTeX XMLCite \textit{C. Boonyasiriwat} et al., Math. Comput. 80, No. 275, 1703--1723 (2011; Zbl 1220.65064) Full Text: DOI
Bai, Yihua; Ward, Robert C. Parallel block tridiagonalization of real symmetric matrices. (English) Zbl 1243.65174 J. Parallel Distrib. Comput. 68, No. 5, 703-715 (2008). MSC: 65Y05 65F15 65F30 PDFBibTeX XMLCite \textit{Y. Bai} and \textit{R. C. Ward}, J. Parallel Distrib. Comput. 68, No. 5, 703--715 (2008; Zbl 1243.65174) Full Text: DOI
Kaya, Doǧan Parallel algorithms for reduction of a symmetric matrix to tridiagonal form on a shared memory multiprocessor. (English) Zbl 1082.65522 Appl. Math. Comput. 169, No. 2, 1045-1062 (2005). MSC: 65F30 65Y05 15A21 65F15 PDFBibTeX XMLCite \textit{D. Kaya}, Appl. Math. Comput. 169, No. 2, 1045--1062 (2005; Zbl 1082.65522) Full Text: DOI
Bini, Dario A.; Gemignani, Luca; Pan, Victor Y. Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations. (English) Zbl 1072.65068 Numer. Math. 100, No. 3, 373-408 (2005). Reviewer: Constantin Popa (Constanta) MSC: 65H05 65F15 12Y05 30C15 26D10 PDFBibTeX XMLCite \textit{D. A. Bini} et al., Numer. Math. 100, No. 3, 373--408 (2005; Zbl 1072.65068) Full Text: DOI
Kaya, Doǧan The symmetric tridiagonal eigenproblem on a shared memory multiprocessor. II. (English) Zbl 1068.65047 Appl. Math. Comput. 163, No. 1, 213-244 (2005). MSC: 65F15 65F50 65Y05 65Y15 PDFBibTeX XMLCite \textit{D. Kaya}, Appl. Math. Comput. 163, No. 1, 213--244 (2005; Zbl 1068.65047) Full Text: DOI
Kaya, Doǧan The symmetric tridigonal eigenproblem on a shared memory multiprocessor. I. (English) Zbl 1057.65017 Appl. Math. Comput. 156, No. 1, 189-209 (2004). MSC: 65F15 65Y05 68N19 65Y15 PDFBibTeX XMLCite \textit{D. Kaya}, Appl. Math. Comput. 156, No. 1, 189--209 (2004; Zbl 1057.65017) Full Text: DOI
Elhay, S.; Golub, G. H.; Ram, Y. M. The spectrum of a modified linear pencil. (English) Zbl 1054.65033 Comput. Math. Appl. 46, No. 8-9, 1413-1426 (2003). Reviewer: Yueh-er Kuo (Knoxville) MSC: 65F15 15A18 15A21 15B48 PDFBibTeX XMLCite \textit{S. Elhay} et al., Comput. Math. Appl. 46, No. 8--9, 1413--1426 (2003; Zbl 1054.65033) Full Text: DOI
Melman, A. Analysis of third-order methods for secular equations. (English) Zbl 0899.65028 Math. Comput. 67, No. 221, 271-286 (1998). Reviewer: Z.Dostal (Ostrava) MSC: 65H05 65F15 65D25 PDFBibTeX XMLCite \textit{A. Melman}, Math. Comput. 67, No. 221, 271--286 (1998; Zbl 0899.65028) Full Text: DOI
Melman, A. A unifying convergence analysis of second-order methods for secular equations. (English) Zbl 0854.65032 Math. Comput. 66, No. 217, 333-344 (1997). MSC: 65F15 65H05 PDFBibTeX XMLCite \textit{A. Melman}, Math. Comput. 66, No. 217, 333--344 (1997; Zbl 0854.65032) Full Text: DOI
Melman, A. A numerical comparison of methods for solving secular equations. (English) Zbl 0889.65037 J. Comput. Appl. Math. 86, No. 1, 237-249 (1997). Reviewer: Z.Dostál (Ostrava) MSC: 65F15 65H05 PDFBibTeX XMLCite \textit{A. Melman}, J. Comput. Appl. Math. 86, No. 1, 237--249 (1997; Zbl 0889.65037) Full Text: DOI
Baldridge, Kim K. Parallel implementation of semiempirical quantum methods for the Intel platforms. (English) Zbl 1076.81501 J. Math. Chem. 19, No. 1, 87-109 (1996). MSC: 81-08 PDFBibTeX XMLCite \textit{K. K. Baldridge}, J. Math. Chem. 19, No. 1, 87--109 (1996; Zbl 1076.81501) Full Text: DOI
Li, Kuiyuan; Li, Tien-Yien; Zeng, Zhonggang An algorithm for the generalized symmetric tridiagonal eigenvalue problem. (English) Zbl 0821.65018 Numer. Algorithms 8, No. 2-4, 269-291 (1994). Reviewer: L.P.Lebedev (Rostov-na-Donu) MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{K. Li} et al., Numer. Algorithms 8, No. 2--4, 269--291 (1994; Zbl 0821.65018) Full Text: DOI
Jessup, E. R. A case against a divide and conquer approach to the nonsymmetric eigenvalue problem. (English) Zbl 0782.65052 Appl. Numer. Math. 12, No. 5, 403-420 (1993). Reviewer: J.Zítko (Praha) MSC: 65F15 65Y05 65H05 30C15 PDFBibTeX XMLCite \textit{E. R. Jessup}, Appl. Numer. Math. 12, No. 5, 403--420 (1993; Zbl 0782.65052) Full Text: DOI
Swarztrauber, Paul N. A parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix. (English) Zbl 0777.65023 Math. Comput. 60, No. 202, 651-668 (1993). Reviewer: P.K.Mahanti (Ranchi) MSC: 65F15 65Y05 PDFBibTeX XMLCite \textit{P. N. Swarztrauber}, Math. Comput. 60, No. 202, 651--668 (1993; Zbl 0777.65023) Full Text: DOI
Bini, D.; Pan, V. Practical improvement of the divide-and-conquer eigenvalue algorithms. (English) Zbl 0756.65053 Computing 48, No. 1, 109-123 (1992). Reviewer: I.N.Molchanov (Kiev) MSC: 65F15 65Y20 PDFBibTeX XMLCite \textit{D. Bini} and \textit{V. Pan}, Computing 48, No. 1, 109--123 (1992; Zbl 0756.65053) Full Text: DOI
Li, T. Y.; Zeng, Zhonggang Homotopy-determinant algorithm for solving nonsymmetric eigenvalue problems. (English) Zbl 0783.65034 Math. Comput. 59, No. 200, 483-502 (1992). Reviewer: W.Gander (Zürich) MSC: 65F15 65H17 65Y05 65F40 PDFBibTeX XMLCite \textit{T. Y. Li} and \textit{Z. Zeng}, Math. Comput. 59, No. 200, 483--502 (1992; Zbl 0783.65034) Full Text: DOI
Benasseni, J. A note on bounds to the variation of eigenvalues in symmetric matrix perturbation of rank one. (English) Zbl 0709.15017 Linear Multilinear Algebra 27, No. 2, 111-116 (1990). Reviewer: Z.Dostál MSC: 15A42 15B57 PDFBibTeX XMLCite \textit{J. Benasseni}, Linear Multilinear Algebra 27, No. 2, 111--116 (1990; Zbl 0709.15017) Full Text: DOI
Pini, G. Computation of minimum eigenvalue through minimization of Rayleigh’s quotient for large sparse matrices using vector computer. (English) Zbl 0706.65031 Int. J. Comput. Math. 36, No. 1-2, 89-99 (1990). Reviewer: A.Ruhe MSC: 65F15 65Y05 PDFBibTeX XMLCite \textit{G. Pini}, Int. J. Comput. Math. 36, No. 1--2, 89--99 (1990; Zbl 0706.65031) Full Text: DOI
Kalamboukis, T. Z. Tridiagonalization of band symmetric matrices for vector computers. (English) Zbl 0704.65031 Comput. Math. Appl. 19, No. 2, 29-34 (1990). Reviewer: J.Albrycht MSC: 65F35 65Y05 65Y20 65F50 PDFBibTeX XMLCite \textit{T. Z. Kalamboukis}, Comput. Math. Appl. 19, No. 2, 29--34 (1990; Zbl 0704.65031) Full Text: DOI
Berry, Michael; Sameh, Ahmed An overview of parallel algorithms for the singular value and symmetric eigenvalue problems. (English) Zbl 0676.65030 J. Comput. Appl. Math. 27, No. 1-2, 191-213 (1989). Reviewer: V.Burjan MSC: 65F15 65Y05 PDFBibTeX XMLCite \textit{M. Berry} and \textit{A. Sameh}, J. Comput. Appl. Math. 27, No. 1--2, 191--213 (1989; Zbl 0676.65030) Full Text: DOI
Beattie, Christopher; Fox, David W. Schur complements and the Weinstein-Aronszajn theory for modified matrix eigenvalue problems. (English) Zbl 0661.15008 Linear Algebra Appl. 108, 37-61 (1988). Reviewer: E.Kreyszig MSC: 15A18 65F15 15A42 49R50 PDFBibTeX XMLCite \textit{C. Beattie} and \textit{D. W. Fox}, Linear Algebra Appl. 108, 37--61 (1988; Zbl 0661.15008) Full Text: DOI