Mastronardi, Nicola; van Barel, Marc; Vandebril, Raf; van Dooren, Paul Deflating invariant subspaces for rank structured pencils. (English) Zbl 07808048 Electron. J. Linear Algebra 40, 177-202 (2024). Reviewer: Steven B. Damelin (Ann Arbor) MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., Electron. J. Linear Algebra 40, 177--202 (2024; Zbl 07808048) Full Text: DOI
Mastronardi, Nicola; Van Barel, Marc; Vandebril, Raf; Van Dooren, Paul Rational QZ steps with perfect shifts. (English) Zbl 07806994 Numer. Algorithms 95, No. 3, 1079-1102 (2024). MSC: 65F15 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., Numer. Algorithms 95, No. 3, 1079--1102 (2024; Zbl 07806994) Full Text: DOI OA License
Concas, Anna; Fenu, Caterina; Rodriguez, Giuseppe; Vandebril, Raf The seriation problem in the presence of a double Fiedler value. (English) Zbl 1507.65077 Numer. Algorithms 92, No. 1, 407-435 (2023). MSC: 65F15 65F50 05C82 91D30 PDFBibTeX XMLCite \textit{A. Concas} et al., Numer. Algorithms 92, No. 1, 407--435 (2023; Zbl 1507.65077) Full Text: DOI arXiv
Van Barel, Marc; Van Buggenhout, Niel; Vandebril, Raf Algorithms for Modifying Recurrence Relations of Orthogonal Polynomial and Rational Functions when Changing the Discrete Inner Product. arXiv:2302.00355 Preprint, arXiv:2302.00355 [math.NA] (2023). MSC: 15A22 65F18 65Q30 33C45 41A20 41A10 BibTeX Cite \textit{M. Van Barel} et al., ``Algorithms for Modifying Recurrence Relations of Orthogonal Polynomial and Rational Functions when Changing the Discrete Inner Product'', Preprint, arXiv:2302.00355 [math.NA] (2023) Full Text: DOI arXiv OA License
Steel, Thijs; Vandebril, Raf A novel, blocked algorithm for the reduction to Hessenberg-triangular form. (English) Zbl 1510.65071 Electron. J. Linear Algebra 38, 712-728 (2022). MSC: 65F15 15A18 65Y10 PDFBibTeX XMLCite \textit{T. Steel} and \textit{R. Vandebril}, Electron. J. Linear Algebra 38, 712--728 (2022; Zbl 1510.65071) Full Text: Link
Van Buggenhout, Niel; Van Barel, Marc; Vandebril, Raf Generation of orthogonal rational functions by procedures for structured matrices. (English) Zbl 1480.65103 Numer. Algorithms 89, No. 2, 551-582 (2022). MSC: 65F60 65F18 30C10 PDFBibTeX XMLCite \textit{N. Van Buggenhout} et al., Numer. Algorithms 89, No. 2, 551--582 (2022; Zbl 1480.65103) Full Text: DOI arXiv Link
Steel, Thijs; Vandebril, Raf; Langou, Julien A new deflation criterion for the QZ algorithm. arXiv:2208.02057 Preprint, arXiv:2208.02057 [math.NA] (2022). MSC: 65F15 BibTeX Cite \textit{T. Steel} et al., ``A new deflation criterion for the QZ algorithm'', Preprint, arXiv:2208.02057 [math.NA] (2022) Full Text: DOI arXiv OA License
Noferini, Vanni; Robol, Leonardo; Vandebril, Raf Structured backward errors in linearizations. (English) Zbl 1470.65093 ETNA, Electron. Trans. Numer. Anal. 54, 420-442 (2021). MSC: 65H04 65F35 PDFBibTeX XMLCite \textit{V. Noferini} et al., ETNA, Electron. Trans. Numer. Anal. 54, 420--442 (2021; Zbl 1470.65093) Full Text: DOI arXiv Link
Steel, Thijs; Camps, Daan; Meerbergen, Karl; Vandebril, Raf A multishift, multipole rational QZ method with aggressive early deflation. (English) Zbl 1467.65032 SIAM J. Matrix Anal. Appl. 42, No. 2, 753-774 (2021). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{T. Steel} et al., SIAM J. Matrix Anal. Appl. 42, No. 2, 753--774 (2021; Zbl 1467.65032) Full Text: DOI arXiv
Dopico, Froilán (ed.); Kressner, Daniel (ed.); Mastronardi, Nicola (ed.); Mehrmann, Volker (ed.); Vandebril, Raf (ed.) Preface. (English) Zbl 1461.01016 Linear Algebra Appl. 623, 1-13 (2021). MSC: 01A70 00B30 15-06 65-06 PDFBibTeX XMLCite \textit{F. Dopico} (ed.) et al., Linear Algebra Appl. 623, 1--13 (2021; Zbl 1461.01016) Full Text: DOI
Mach, Thomas; Steel, Thijs; Vandebril, Raf; Watkins, David S. Pole-swapping algorithms for alternating and palindromic eigenvalue problems. (English) Zbl 1461.93179 Vietnam J. Math. 48, No. 4, 679-701 (2020). MSC: 93B60 93B55 15A22 PDFBibTeX XMLCite \textit{T. Mach} et al., Vietnam J. Math. 48, No. 4, 679--701 (2020; Zbl 1461.93179) Full Text: DOI arXiv
Camps, Daan; Mach, Thomas; Vandebril, Raf; Watkins, David S. On pole-swapping algorithms for the eigenvalue problem. (English) Zbl 1456.65025 ETNA, Electron. Trans. Numer. Anal. 52, 480-508 (2020). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{D. Camps} et al., ETNA, Electron. Trans. Numer. Anal. 52, 480--508 (2020; Zbl 1456.65025) Full Text: DOI arXiv Link
Camps, Daan; Mastronardi, Nicola; Vandebril, Raf; Van Dooren, Paul Swapping \(2 \times 2\) blocks in the Schur and generalized Schur form. (English) Zbl 1524.65161 J. Comput. Appl. Math. 373, Article ID 112274, 8 p. (2020). MSC: 65F15 15A21 PDFBibTeX XMLCite \textit{D. Camps} et al., J. Comput. Appl. Math. 373, Article ID 112274, 8 p. (2020; Zbl 1524.65161) Full Text: DOI
Del Corso, Gianna M.; Poloni, Federico; Robol, Leonardo; Vandebril, Raf Factoring block Fiedler companion matrices. (English) Zbl 1443.15008 Bini, Dario Andrea (ed.) et al., Structured matrices in numerical linear algebra. Analysis, algorithms and applications. Selected papers of the INdAM meeting on structured matrices in numerical linear algebra: analysis, algorithms and applications, Cortona, Italy, September 4–8, 2017. Cham: Springer. Springer INdAM Ser. 30, 129-155 (2019). MSC: 15A23 PDFBibTeX XMLCite \textit{G. M. Del Corso} et al., Springer INdAM Ser. 30, 129--155 (2019; Zbl 1443.15008) Full Text: DOI
van Buggenhout, Niel; van Barel, Marc; Vandebril, Raf Biorthogonal rational Krylov subspace methods. (English) Zbl 1433.65058 ETNA, Electron. Trans. Numer. Anal. 51, 451-468 (2019). MSC: 65F15 15A22 65Q30 PDFBibTeX XMLCite \textit{N. van Buggenhout} et al., ETNA, Electron. Trans. Numer. Anal. 51, 451--468 (2019; Zbl 1433.65058) Full Text: DOI arXiv Link
Del Corso, Gianna M.; Poloni, Federico; Robol, Leonardo; Vandebril, Raf When is a matrix unitary or Hermitian plus low rank? (English) Zbl 1463.15075 Numer. Linear Algebra Appl. 26, No. 6, e2266, 19 p. (2019). MSC: 15B57 15A21 65F55 PDFBibTeX XMLCite \textit{G. M. Del Corso} et al., Numer. Linear Algebra Appl. 26, No. 6, e2266, 19 p. (2019; Zbl 1463.15075) Full Text: DOI arXiv Link
Camps, Daan; Meerbergen, Karl; Vandebril, Raf A rational QZ method. (English) Zbl 1420.65044 SIAM J. Matrix Anal. Appl. 40, No. 3, 943-972 (2019). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{D. Camps} et al., SIAM J. Matrix Anal. Appl. 40, No. 3, 943--972 (2019; Zbl 1420.65044) Full Text: DOI arXiv
Camps, Daan; Meerbergen, Karl; Vandebril, Raf An implicit filter for rational Krylov using core transformations. (English) Zbl 1403.65016 Linear Algebra Appl. 561, 113-140 (2019). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{D. Camps} et al., Linear Algebra Appl. 561, 113--140 (2019; Zbl 1403.65016) Full Text: DOI Link
Aurentz, Jared; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S. Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials. (English) Zbl 1434.65030 Math. Comput. 88, No. 315, 313-347 (2019). Reviewer: Martin Plešinger (Liberec) MSC: 65F15 15A22 15A18 PDFBibTeX XMLCite \textit{J. Aurentz} et al., Math. Comput. 88, No. 315, 313--347 (2019; Zbl 1434.65030) Full Text: DOI arXiv
Robol, Leonardo; Vandebril, Raf Efficient Ehrlich-Aberth iteration for finding intersections of interpolating polynomials and rational functions. (English) Zbl 1416.65096 Linear Algebra Appl. 542, 282-309 (2018). MSC: 65F15 15A18 65H05 PDFBibTeX XMLCite \textit{L. Robol} and \textit{R. Vandebril}, Linear Algebra Appl. 542, 282--309 (2018; Zbl 1416.65096) Full Text: DOI
Farenick, D. (ed.); Lemmens, B. (ed.); Van Barel, M. (ed.); Vandebril, R. (ed.) Preface to the proceedings of the 20th ILAS meeting, Leuven, Belgium, 2016. (English) Zbl 1416.00032 Linear Algebra Appl. 542, 1-3 (2018). MSC: 00B25 15-06 PDFBibTeX XMLCite \textit{D. Farenick} (ed.) et al., Linear Algebra Appl. 542, 1--3 (2018; Zbl 1416.00032) Full Text: DOI Link
Aurentz, Jared L.; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S. Core-chasing algorithms for the eigenvalue problem. (English) Zbl 1434.65003 Fundamentals of Algorithms 13. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-61197-533-8/pbk; 978-1-61197-534-5). ix, 149 p. (2018). Reviewer: Xueyuan Tan (Nanjing) MSC: 65-02 65F15 65F18 65H17 15A23 PDFBibTeX XMLCite \textit{J. L. Aurentz} et al., Core-chasing algorithms for the eigenvalue problem. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2018; Zbl 1434.65003) Full Text: DOI
Aurentz, Jared L.; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S. Fast and backward stable computation of roots of polynomials. II: Backward error analysis; companion matrix and companion pencil. (English) Zbl 1398.65056 SIAM J. Matrix Anal. Appl. 39, No. 3, 1245-1269 (2018). MSC: 65F15 65H17 15A18 65H04 PDFBibTeX XMLCite \textit{J. L. Aurentz} et al., SIAM J. Matrix Anal. Appl. 39, No. 3, 1245--1269 (2018; Zbl 1398.65056) Full Text: DOI arXiv
Beckermann, Bernhard; Mertens, Clara; Vandebril, Raf On an economic Arnoldi method for \(BML\)-matrices. (English) Zbl 1392.65044 SIAM J. Matrix Anal. Appl. 39, No. 2, 737-768 (2018). MSC: 65F10 65F25 PDFBibTeX XMLCite \textit{B. Beckermann} et al., SIAM J. Matrix Anal. Appl. 39, No. 2, 737--768 (2018; Zbl 1392.65044) Full Text: DOI
Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S. Computing the eigenvalues of symmetric tridiagonal matrices via a Cayley transformation. (English) Zbl 1392.65084 ETNA, Electron. Trans. Numer. Anal. 46, 447-459 (2017). MSC: 65F15 65H17 15A18 15B10 PDFBibTeX XMLCite \textit{J. L. Aurentz} et al., ETNA, Electron. Trans. Numer. Anal. 46, 447--459 (2017; Zbl 1392.65084) Full Text: Link
Ferranti, Micol; Iannazzo, Bruno; Mach, Thomas; Vandebril, Raf An extended Hamiltonian QR algorithm. (English) Zbl 1376.65049 Calcolo 54, No. 3, 1097-1120 (2017). MSC: 65F15 PDFBibTeX XMLCite \textit{M. Ferranti} et al., Calcolo 54, No. 3, 1097--1120 (2017; Zbl 1376.65049) Full Text: DOI Link
Ferranti, Micol; Iannazzo, Bruno; Mach, Thomas; Vandebril, Raf An extended Hessenberg form for Hamiltonian matrices. (English) Zbl 1372.65108 Calcolo 54, No. 1, 423-453 (2017). Reviewer: Constantin Popa (Constanţa) MSC: 65F15 15A18 15A23 PDFBibTeX XMLCite \textit{M. Ferranti} et al., Calcolo 54, No. 1, 423--453 (2017; Zbl 1372.65108) Full Text: DOI Link
Robol, Leonardo; Vandebril, Raf; Van Dooren, Paul A framework for structured linearizations of matrix polynomials in various bases. (English) Zbl 1365.15028 SIAM J. Matrix Anal. Appl. 38, No. 1, 188-216 (2017). MSC: 15A54 15A22 PDFBibTeX XMLCite \textit{L. Robol} et al., SIAM J. Matrix Anal. Appl. 38, No. 1, 188--216 (2017; Zbl 1365.15028) Full Text: DOI arXiv
Beckermann, Bernhard; Mertens, Clara; Vandebril, Raf On a fast Arnoldi method for BML matrices. arXiv:1702.00671 Preprint, arXiv:1702.00671 [math.NA] (2017). BibTeX Cite \textit{B. Beckermann} et al., ``On a fast Arnoldi method for BML matrices'', Preprint, arXiv:1702.00671 [math.NA] (2017) Full Text: arXiv OA License
Jagels, Carl; Mach, Thomas; Reichel, Lothar; Vandebril, Raf Convergence rates for inverse-free rational approximation of matrix functions. (English) Zbl 1352.65135 Linear Algebra Appl. 510, 291-310 (2016). MSC: 65F60 65F10 47J25 15A16 PDFBibTeX XMLCite \textit{C. Jagels} et al., Linear Algebra Appl. 510, 291--310 (2016; Zbl 1352.65135) Full Text: DOI
Jeuris, B.; Vandebril, R. The Kähler mean of block-Toeplitz matrices with Toeplitz structured blocks. (English) Zbl 1347.15035 SIAM J. Matrix Anal. Appl. 37, No. 3, 1151-1175 (2016). MSC: 15B05 26E60 53B21 65F30 PDFBibTeX XMLCite \textit{B. Jeuris} and \textit{R. Vandebril}, SIAM J. Matrix Anal. Appl. 37, No. 3, 1151--1175 (2016; Zbl 1347.15035) Full Text: DOI
Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S. A note on companion pencils. (English) Zbl 1347.65068 da Fonseca, Carlos M. et al., A panorama of mathematics: pure and applied. Conference mathematics and its applications, Kuwait University, Safat, Kuwait, November 14–17, 2014. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1668-3/pbk; 978-1-4704-2902-7/ebook). Contemporary Mathematics 658, 91-101 (2016). MSC: 65F15 15A23 PDFBibTeX XMLCite \textit{J. L. Aurentz} et al., Contemp. Math. 658, 91--101 (2016; Zbl 1347.65068) Full Text: DOI Link
Mach, T.; Reichel, L.; Van Barel, M.; Vandebril, R. Adaptive cross approximation for ill-posed problems. (English) Zbl 1416.65565 J. Comput. Appl. Math. 303, 206-217 (2016). MSC: 65R32 45Q05 65F50 65F15 PDFBibTeX XMLCite \textit{T. Mach} et al., J. Comput. Appl. Math. 303, 206--217 (2016; Zbl 1416.65565) Full Text: DOI
Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S. Fast and stable unitary QR algorithm. (English) Zbl 1327.65071 ETNA, Electron. Trans. Numer. Anal. 44, 327-341 (2015). MSC: 65F15 65H17 15A18 15B10 PDFBibTeX XMLCite \textit{J. L. Aurentz} et al., ETNA, Electron. Trans. Numer. Anal. 44, 327--341 (2015; Zbl 1327.65071) Full Text: EMIS
Mertens, Clara; Vandebril, Raf Short recurrences for computing extended Krylov bases for Hermitian and unitary matrices. (English) Zbl 1330.65063 Numer. Math. 131, No. 2, 303-328 (2015). Reviewer: Michael Jung (Dresden) MSC: 65F25 15A23 15B10 15B57 65F50 PDFBibTeX XMLCite \textit{C. Mertens} and \textit{R. Vandebril}, Numer. Math. 131, No. 2, 303--328 (2015; Zbl 1330.65063) Full Text: DOI Link
Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S. Fast and backward stable computation of roots of polynomials. (English) Zbl 1319.65034 SIAM J. Matrix Anal. Appl. 36, No. 3, 942-973 (2015). MSC: 65H04 65F15 PDFBibTeX XMLCite \textit{J. L. Aurentz} et al., SIAM J. Matrix Anal. Appl. 36, No. 3, 942--973 (2015; Zbl 1319.65034) Full Text: DOI Link
Vannieuwenhoven, Nick; Meerbergen, Karl; Vandebril, Raf Computing the gradient in optimization algorithms for the CP decomposition in constant memory through tensor blocking. (English) Zbl 1320.65066 SIAM J. Sci. Comput. 37, No. 3, C415-C438 (2015). MSC: 65F30 15A69 65Y20 65K10 68W30 PDFBibTeX XMLCite \textit{N. Vannieuwenhoven} et al., SIAM J. Sci. Comput. 37, No. 3, C415--C438 (2015; Zbl 1320.65066) Full Text: DOI
Vannieuwenhoven, Nick; Vandebril, Raf; Meerbergen, Karl A randomized algorithm for testing nonsingularity of structured matrices with an application to asserting nondefectivity of Segre varieties. (English) Zbl 1320.65067 IMA J. Numer. Anal. 35, No. 1, 289-324 (2015). Reviewer: Edgar Pereira (Natal) MSC: 65F30 14Q15 PDFBibTeX XMLCite \textit{N. Vannieuwenhoven} et al., IMA J. Numer. Anal. 35, No. 1, 289--324 (2015; Zbl 1320.65067) Full Text: DOI
Mertens, Clara; Vandebril, Raf Multiple recurrences and the associated matrix structures stemming from normal matrices. (English) Zbl 1312.65049 SIAM J. Numer. Anal. 52, No. 6, 2977-2999 (2014). MSC: 65F10 65F25 PDFBibTeX XMLCite \textit{C. Mertens} and \textit{R. Vandebril}, SIAM J. Numer. Anal. 52, No. 6, 2977--2999 (2014; Zbl 1312.65049) Full Text: DOI Link
Vannieuwenhoven, N.; Nicaise, J.; Vandebril, R.; Meerbergen, K. On generic nonexistence of the Schmidt-Eckart-Young decomposition for complex tensors. (English) Zbl 1311.15027 SIAM J. Matrix Anal. Appl. 35, No. 3, 886-903 (2014). Reviewer: Costică Moroşanu (Iaşi) MSC: 15A69 15A21 PDFBibTeX XMLCite \textit{N. Vannieuwenhoven} et al., SIAM J. Matrix Anal. Appl. 35, No. 3, 886--903 (2014; Zbl 1311.15027) Full Text: DOI Link
Mach, Thomas; Pranić, Miroslav S.; Vandebril, Raf Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices. (English) Zbl 1302.65078 ETNA, Electron. Trans. Numer. Anal. 43(2014-2015), 100-124 (2014). MSC: 65F10 65F30 65F60 15A24 PDFBibTeX XMLCite \textit{T. Mach} et al., ETNA, Electron. Trans. Numer. Anal. 43, 100--124 (2014; Zbl 1302.65078) Full Text: EMIS
Mach, Thomas; Vandebril, Raf On deflations in extended QR algorithms. (English) Zbl 1301.65025 SIAM J. Matrix Anal. Appl. 35, No. 2, 559-579 (2014). MSC: 65F15 PDFBibTeX XMLCite \textit{T. Mach} and \textit{R. Vandebril}, SIAM J. Matrix Anal. Appl. 35, No. 2, 559--579 (2014; Zbl 1301.65025) Full Text: DOI Link
Ferranti, Micol; Le, Thanh Hieu; Vandebril, Raf A comparison between the complex symmetric based and classical computation of the singular value decomposition of normal matrices. (English) Zbl 1298.65069 Numer. Algorithms 67, No. 1, 109-120 (2014). MSC: 65F20 PDFBibTeX XMLCite \textit{M. Ferranti} et al., Numer. Algorithms 67, No. 1, 109--120 (2014; Zbl 1298.65069) Full Text: DOI Link
Mach, Thomas; Van Barel, Marc; Vandebril, Raf Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices. (English) Zbl 1294.65041 J. Comput. Appl. Math. 272, 377-398 (2014). MSC: 65F18 65F25 65F50 PDFBibTeX XMLCite \textit{T. Mach} et al., J. Comput. Appl. Math. 272, 377--398 (2014; Zbl 1294.65041) Full Text: DOI
Ferranti, Micol; Vandebril, Raf Computing eigenvalues of normal matrices via complex symmetric matrices. (English) Zbl 1291.65119 J. Comput. Appl. Math. 259, Part A, 281-293 (2014). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{M. Ferranti} and \textit{R. Vandebril}, J. Comput. Appl. Math. 259, Part A, 281--293 (2014; Zbl 1291.65119) Full Text: DOI
Bini, Dario A.; Iannazzo, Bruno; Jeuris, Ben; Vandebril, Raf Geometric means of structured matrices. (English) Zbl 1291.15034 BIT 54, No. 1, 55-83 (2014). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15A24 14Q10 15B05 53B21 65K10 26E60 47A64 PDFBibTeX XMLCite \textit{D. A. Bini} et al., BIT 54, No. 1, 55--83 (2014; Zbl 1291.15034) Full Text: DOI Link
Aurentz, Jared L.; Vandebril, Raf; Watkins, David S. Fast computation of eigenvalues of companion, comrade, and related matrices. (English) Zbl 1293.65052 BIT 54, No. 1, 7-30 (2014). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F15 65H04 PDFBibTeX XMLCite \textit{J. L. Aurentz} et al., BIT 54, No. 1, 7--30 (2014; Zbl 1293.65052) Full Text: DOI
Mach, Thomas; Pranić, Miroslav S.; Vandebril, Raf Computing approximate extended Krylov subspaces without explicit inversion. (English) Zbl 1305.65138 ETNA, Electron. Trans. Numer. Anal. 40, 414-435 (2013). MSC: 65F60 65F10 47J25 15A16 PDFBibTeX XMLCite \textit{T. Mach} et al., ETNA, Electron. Trans. Numer. Anal. 40, 414--435 (2013; Zbl 1305.65138) Full Text: EMIS
Vandebril, Raf; Watkins, David S. An extension of the \(QZ\) algorithm beyond the Hessenberg-upper triangular pencil. (English) Zbl 1288.65053 ETNA, Electron. Trans. Numer. Anal. 40, 17-35 (2013). MSC: 65F15 PDFBibTeX XMLCite \textit{R. Vandebril} and \textit{D. S. Watkins}, ETNA, Electron. Trans. Numer. Anal. 40, 17--35 (2013; Zbl 1288.65053) Full Text: EMIS
Jeuris, Ben; Vandebril, Raf Geometric mean algorithms based on harmonic and arithmetic iterations. (English) Zbl 1322.65053 Nielsen, Frank (ed.) et al., Geometric science of information. First international conference, GSI 2013, Paris, France, August 28–30, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-40019-3/pbk). Lecture Notes in Computer Science 8085, 785-793 (2013). MSC: 65F30 15B48 PDFBibTeX XMLCite \textit{B. Jeuris} and \textit{R. Vandebril}, Lect. Notes Comput. Sci. 8085, 785--793 (2013; Zbl 1322.65053) Full Text: DOI Link
Aurentz, Jared L.; Vandebril, Raf; Watkins, David S. Fast computation of the zeros of a polynomial via factorization of the companion matrix. (English) Zbl 1264.65074 SIAM J. Sci. Comput. 35, No. 1, A255-A269 (2013). MSC: 65H04 65F15 PDFBibTeX XMLCite \textit{J. L. Aurentz} et al., SIAM J. Sci. Comput. 35, No. 1, A255--A269 (2013; Zbl 1264.65074) Full Text: DOI
Jeuris, Ben; Vandebril, Raf; Vandereycken, Bart A survey and comparison of contemporary algorithms for computing the matrix geometric mean. (English) Zbl 1287.65036 ETNA, Electron. Trans. Numer. Anal. 39, 379-402 (2012). MSC: 65F60 47A64 15A60 65K10 15B48 PDFBibTeX XMLCite \textit{B. Jeuris} et al., ETNA, Electron. Trans. Numer. Anal. 39, 379--402 (2012; Zbl 1287.65036) Full Text: EMIS
Vandebril, Raf; Watkins, David S. A generalization of the multishift QR algorithm. (English) Zbl 1261.65039 SIAM J. Matrix Anal. Appl. 33, No. 3, 759-779 (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65F15 PDFBibTeX XMLCite \textit{R. Vandebril} and \textit{D. S. Watkins}, SIAM J. Matrix Anal. Appl. 33, No. 3, 759--779 (2012; Zbl 1261.65039) Full Text: DOI
Vannieuwenhoven, Nick; Vandebril, Raf; Meerbergen, Karl A new truncation strategy for the higher-order singular value decomposition. (English) Zbl 1247.65055 SIAM J. Sci. Comput. 34, No. 2, A1027-A1052 (2012). MSC: 65F20 15A69 PDFBibTeX XMLCite \textit{N. Vannieuwenhoven} et al., SIAM J. Sci. Comput. 34, No. 2, A1027--A1052 (2012; Zbl 1247.65055) Full Text: DOI Link
Meerbergen, Karl; Vandebril, Raf A reflection on the implicitly restarted Arnoldi method for computing eigenvalues near a vertical line. (English) Zbl 1247.65049 Linear Algebra Appl. 436, No. 8, 2828-2844 (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{K. Meerbergen} and \textit{R. Vandebril}, Linear Algebra Appl. 436, No. 8, 2828--2844 (2012; Zbl 1247.65049) Full Text: DOI
Vandebril, Raf; Del Corso, Gianna M. A unification of unitary similarity transforms to compressed representations. (English) Zbl 1231.65075 Numer. Math. 119, No. 4, 641-665 (2011). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65F30 15A21 65F10 65F15 PDFBibTeX XMLCite \textit{R. Vandebril} and \textit{G. M. Del Corso}, Numer. Math. 119, No. 4, 641--665 (2011; Zbl 1231.65075) Full Text: DOI Link
Vandebril, Raf Chasing bulges or rotations? A metamorphosis of the QR-algorithm. (English) Zbl 1218.65035 SIAM J. Matrix Anal. Appl. 32, No. 1, 217-247 (2011). MSC: 65F15 PDFBibTeX XMLCite \textit{R. Vandebril}, SIAM J. Matrix Anal. Appl. 32, No. 1, 217--247 (2011; Zbl 1218.65035) Full Text: DOI Link
Vandebril, Raf A unitary similarity transform of a normal matrix to complex symmetric form. (English) Zbl 1203.15009 Appl. Math. Lett. 24, No. 2, 160-164 (2011). MSC: 15A21 15B57 PDFBibTeX XMLCite \textit{R. Vandebril}, Appl. Math. Lett. 24, No. 2, 160--164 (2011; Zbl 1203.15009) Full Text: DOI
Vandebril, Raf; Del Corso, Gianna M. An implicit multishift \(QR\)-algorithm for Hermitian plus low rank matrices. (English) Zbl 1216.65045 SIAM J. Sci. Comput. 32, No. 4, 2190-2212 (2010). MSC: 65F15 PDFBibTeX XMLCite \textit{R. Vandebril} and \textit{G. M. Del Corso}, SIAM J. Sci. Comput. 32, No. 4, 2190--2212 (2010; Zbl 1216.65045) Full Text: DOI
Beckermann, Bernhard; Güttel, Stefan; Vandebril, Raf On the convergence of rational Ritz values. (English) Zbl 1213.15009 SIAM J. Matrix Anal. Appl. 31, No. 4, 1740-1774 (2010). Reviewer: Axel Ruhe (Stockholm) MSC: 15A18 65F15 31A15 15B05 PDFBibTeX XMLCite \textit{B. Beckermann} et al., SIAM J. Matrix Anal. Appl. 31, No. 4, 1740--1774 (2010; Zbl 1213.15009) Full Text: DOI
Van Barel, Marc; Vandebril, Raf; Van Dooren, Paul; Frederix, Katrijn Implicit double shift \(QR\)-algorithm for companion matrices. (English) Zbl 1196.65076 Numer. Math. 116, No. 2, 177-212 (2010). MSC: 65F15 PDFBibTeX XMLCite \textit{M. Van Barel} et al., Numer. Math. 116, No. 2, 177--212 (2010; Zbl 1196.65076) Full Text: DOI
Vandebril, Raf On tridiagonal matrices unitarily equivalent to normal matrices. (English) Zbl 1221.15058 Linear Algebra Appl. 432, No. 12, 3079-3099 (2010). Reviewer: Václav Burjan (Praha) MSC: 15B57 15A23 15A21 65F30 65F20 PDFBibTeX XMLCite \textit{R. Vandebril}, Linear Algebra Appl. 432, No. 12, 3079--3099 (2010; Zbl 1221.15058) Full Text: DOI
Vandebril, Raf; van Barel, Marc; Mastronardi, Nicola A multiple shift \(QR\)-step for structured rank matrices. (English) Zbl 1179.65041 J. Comput. Appl. Math. 233, No. 5, 1326-1344 (2010). MSC: 65F15 PDFBibTeX XMLCite \textit{R. Vandebril} et al., J. Comput. Appl. Math. 233, No. 5, 1326--1344 (2010; Zbl 1179.65041) Full Text: DOI
Mastronardi, Nicola; Van Barel, Marc; Vandebril, Raf On the computation of the null space of Toeplitz-like matrices. (English) Zbl 1188.65026 ETNA, Electron. Trans. Numer. Anal. 33(2008-2009), 151-162 (2009). MSC: 65F05 15B05 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., ETNA, Electron. Trans. Numer. Anal. 33, 151--162 (2009; Zbl 1188.65026) Full Text: EuDML EMIS
Vandebril, Raf; Van Barel, Marc; Mastronardi, Nicola A new iteration for computing the eigenvalues of semiseparable (plus diagonal) matrices. (English) Zbl 1188.65047 ETNA, Electron. Trans. Numer. Anal. 33(2008-2009), 126-150 (2009). MSC: 65F15 PDFBibTeX XMLCite \textit{R. Vandebril} et al., ETNA, Electron. Trans. Numer. Anal. 33, 126--150 (2009; Zbl 1188.65047) Full Text: EuDML EMIS
Vandebril, Raf; Golub, Gene; van Barel, Marc A quasi-separable approach to solve the symmetric definite tridiagonal generalized eigenvalue problem. (English) Zbl 1186.65046 SIAM J. Matrix Anal. Appl. 31, No. 1, 154-174 (2009). MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{R. Vandebril} et al., SIAM J. Matrix Anal. Appl. 31, No. 1, 154--174 (2009; Zbl 1186.65046) Full Text: DOI Link
Mastronardi, N.; Van Barel, M.; Vandebril, R. A fast algorithm for computing the smallest eigenvalue of a symmetric positive-definite Toeplitz matrix. (English) Zbl 1212.65153 Numer. Linear Algebra Appl. 15, No. 4, 327-337 (2008). MSC: 65F15 65F50 15B05 94A12 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., Numer. Linear Algebra Appl. 15, No. 4, 327--337 (2008; Zbl 1212.65153) Full Text: DOI
Vandebril, Raf; Van Barel, Marc; Mastronardi, Nicola A parallel QR-factorization/solver of quasiseparable matrices. (English) Zbl 1171.65017 ETNA, Electron. Trans. Numer. Anal. 30, 144-167 (2008). MSC: 65F05 65Y05 PDFBibTeX XMLCite \textit{R. Vandebril} et al., ETNA, Electron. Trans. Numer. Anal. 30, 144--167 (2008; Zbl 1171.65017) Full Text: EuDML EMIS
Vandebril, Raf; Van Barel, Marc; Mastronardi, Nicola Matrix computations and semiseparable matrices. Vol. 2: Eigenvalue and singular value methods. (English) Zbl 1175.65045 Baltimore, MD: Johns Hopkins University Press (ISBN 978-0-8018-9052-9/hbk). xvi, 498 p. (2008). Reviewer: Dietrich Braess (Bochum) MSC: 65F15 65-02 65F18 65F20 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Matrix computations and semiseparable matrices. Vol. 2: Eigenvalue and singular value methods. Baltimore, MD: Johns Hopkins University Press (2008; Zbl 1175.65045)
Vandebril, Raf; Van Barel, Marc; Mastronardi, Nicola Rational \(QR\)-iteration without inversion. (English) Zbl 1154.65020 Numer. Math. 110, No. 4, 561-575 (2008). MSC: 65F15 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Numer. Math. 110, No. 4, 561--575 (2008; Zbl 1154.65020) Full Text: DOI
Vanberghen, Yvette; Vandebril, Raf; Van Barel, Marc AQZ-method based on semiseparable matrices. (English) Zbl 1153.65038 J. Comput. Appl. Math. 218, No. 2, 482-491 (2008). Reviewer: Raffaella Pavani (Milano) MSC: 65F15 PDFBibTeX XMLCite \textit{Y. Vanberghen} et al., J. Comput. Appl. Math. 218, No. 2, 482--491 (2008; Zbl 1153.65038) Full Text: DOI
Mastronardi, N.; Van Barel, M.; Vandebril, R. A fast algorithm for the recursive calculation of dominant singular subspaces. (English) Zbl 1154.65319 J. Comput. Appl. Math. 218, No. 2, 238-246 (2008). MSC: 65F30 15A15 15A09 15A23 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., J. Comput. Appl. Math. 218, No. 2, 238--246 (2008; Zbl 1154.65319) Full Text: DOI
Vandebril, Raf; Van Barel, Marc; Mastronardi, Nicola Matrix computations and semiseparable matrices. Vol. 1: Linear systems. (English) Zbl 1141.65019 Baltimore, MD: Johns Hopkins University Press (ISBN 978-0-8018-8714-7/hbk). xviii, 575 p. (2008). Reviewer: Dietrich Braess (Bochum) MSC: 65Fxx 65-01 15-02 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Matrix computations and semiseparable matrices. Vol. 1: Linear systems. Baltimore, MD: Johns Hopkins University Press (2008; Zbl 1141.65019)
Mastronardi, N.; Van Barel, M.; Vandebril, R. A Schur-based algorithm for computing bounds to the smallest eigenvalue of a symmetric positive definite Toeplitz matrix. (English) Zbl 1136.65042 Linear Algebra Appl. 428, No. 2-3, 479-491 (2008). Reviewer: Raffaella Pavani (Milano) MSC: 65F15 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., Linear Algebra Appl. 428, No. 2--3, 479--491 (2008; Zbl 1136.65042) Full Text: DOI
Vandebril, Raf; Mastronardi, Nicola; Van Barel, Marc Solving linear systems with a Levinson-like solver. (English) Zbl 1171.65366 ETNA, Electron. Trans. Numer. Anal. 26, 243-269 (2007). MSC: 65F05 65Y20 15B57 65F50 PDFBibTeX XMLCite \textit{R. Vandebril} et al., ETNA, Electron. Trans. Numer. Anal. 26, 243--269 (2007; Zbl 1171.65366) Full Text: EuDML EMIS
Vandebril, Raf; Mastronardi, Nicola; Van Barel, Marc A Levinson-like algorithm for symmetric strongly nonsingular higher order semiseparable plus band matrices. (English) Zbl 1102.65032 J. Comput. Appl. Math. 198, No. 1, 75-97 (2007). MSC: 65F05 PDFBibTeX XMLCite \textit{R. Vandebril} et al., J. Comput. Appl. Math. 198, No. 1, 75--97 (2007; Zbl 1102.65032) Full Text: DOI
Vandebril, Raf; Camp, Van Ellen; Van Barel, Marc; Mastronardi, Nicola On the convergence properties of the orthogonal similarity transformations to tridiagonal and semiseparable (plus diagonal) form. (English) Zbl 1102.65042 Numer. Math. 104, No. 2, 205-239 (2006). MSC: 65F15 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Numer. Math. 104, No. 2, 205--239 (2006; Zbl 1102.65042) Full Text: DOI
Vandebril, Raf; Golub, Gene; Van Barel, Marc A small note on the scaling of symmetric positive definite semiseparable matrices. (English) Zbl 1092.65038 Numer. Algorithms 41, No. 3, 319-326 (2006). MSC: 65F35 65F50 65F05 15A12 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Numer. Algorithms 41, No. 3, 319--326 (2006; Zbl 1092.65038) Full Text: DOI Link
Vandebril, Raf; Van Barel, Marc Necessary and sufficient conditions for orthogonal similarity transformations to obtain the Arnoli(Lanczos)-Ritz values. (English) Zbl 1093.65038 Linear Algebra Appl. 414, No. 2-3, 435-444 (2006). Reviewer: Daniel Kressner (Zagreb) MSC: 65F15 65F25 PDFBibTeX XMLCite \textit{R. Vandebril} and \textit{M. Van Barel}, Linear Algebra Appl. 414, No. 2--3, 435--444 (2006; Zbl 1093.65038) Full Text: DOI
Mastronardi, N.; Van Barel, M.; Van Camp, E.; Vandebril, R. On computing the eigenvectors of a class of structured matrices. (English) Zbl 1086.65035 J. Comput. Appl. Math. 189, No. 1-2, 580-591 (2006). MSC: 65F15 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., J. Comput. Appl. Math. 189, No. 1--2, 580--591 (2006; Zbl 1086.65035) Full Text: DOI
Vandebril, Raf; Van Barel, Marc A note on the nullity theorem. (English) Zbl 1090.65038 J. Comput. Appl. Math. 189, No. 1-2, 179-190 (2006). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F05 15A15 65F30 15A03 PDFBibTeX XMLCite \textit{R. Vandebril} and \textit{M. Van Barel}, J. Comput. Appl. Math. 189, No. 1--2, 179--190 (2006; Zbl 1090.65038) Full Text: DOI
Vandebril, Raf; Van Camp, Ellen; Van Barel, Marc; Mastronardi, Nicola Orthogonal similarity transformation of a symmetric matrix into a diagonal-plus-semiseparable one with free choice of the diagonal. (English) Zbl 1086.65040 Numer. Math. 102, No. 4, 709-726 (2006). MSC: 65F30 65Y20 15A21 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Numer. Math. 102, No. 4, 709--726 (2006; Zbl 1086.65040) Full Text: DOI
Vandebril, R.; Van Barel, M.; Golub, G.; Mastronardi, N. A bibliography on semiseparable matrices. (English) Zbl 1168.15312 Calcolo 42, No. 3-4, 249-270 (2005). MSC: 15A99 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Calcolo 42, No. 3--4, 249--270 (2005; Zbl 1168.15312) Full Text: DOI Link
Vandebril, Raf; Van Barel, Marc; Mastronardi, Nicola A note on the representation and definition of semiseparable matrices. (English) Zbl 1164.15341 Numer. Linear Algebra Appl. 12, No. 8, 839-858 (2005). Reviewer: Jan Chleboun (Praha) MSC: 15B57 15A03 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Numer. Linear Algebra Appl. 12, No. 8, 839--858 (2005; Zbl 1164.15341) Full Text: DOI
Vandebril, Raf; Van Barel, Marc; Mastronardi, Nicola An implicit \(QR\) algorithm for symmetric semiseparable matrices. (English) Zbl 1164.65368 Numer. Linear Algebra Appl. 12, No. 7, 625-658 (2005). Reviewer: Jan Chleboun (Praha) MSC: 65F15 65Y20 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Numer. Linear Algebra Appl. 12, No. 7, 625--658 (2005; Zbl 1164.65368) Full Text: DOI
Van Barel, Marc; Vandebril, Raf; Golub, G.; Mastronardi, Nicola A bibliography on semiseparable matrices. (English) Zbl 1168.15306 Calcolo 42, No. 3-4, 249-270 (2005). MSC: 15A21 15A09 PDFBibTeX XMLCite \textit{M. Van Barel} et al., Calcolo 42, No. 3--4, 249--270 (2005; Zbl 1168.15306) Full Text: DOI Link
Mastronardi, Nicola; Schuermans, M.; Van Barel, Marc; Vandebril, Raf; Van Huffel, S. A Lanczos-like reduction of symmetric structured matrices to semiseparable form. (English) Zbl 1150.65010 Calcolo 42, No. 3-4, 227-241 (2005). Reviewer: Petko Hr. Petkov (Sofia) MSC: 65F15 15A21 15A09 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., Calcolo 42, No. 3--4, 227--241 (2005; Zbl 1150.65010) Full Text: DOI
Van Barel, Marc; Vandebril, Raf; Mastronardi, Nicola An implicit \(Q\) theorem for Hessenberg-like matrices. (English) Zbl 1150.15010 Mediterr. J. Math. 2, No. 3, 259-275 (2005). Reviewer: Grozio Stanilov (Sofia) MSC: 15B57 15A18 65F15 PDFBibTeX XMLCite \textit{M. Van Barel} et al., Mediterr. J. Math. 2, No. 3, 259--275 (2005; Zbl 1150.15010) Full Text: DOI
Van Barel, M.; Vandebril, R.; Mastronardi, N. An orthogonal similarity reduction of a matrix into semiseparable form. (English) Zbl 1089.65032 SIAM J. Matrix Anal. Appl. 27, No. 1, 176-197 (2005). Reviewer: Constantin Popa (Constanta) MSC: 65F15 PDFBibTeX XMLCite \textit{M. Van Barel} et al., SIAM J. Matrix Anal. Appl. 27, No. 1, 176--197 (2005; Zbl 1089.65032) Full Text: DOI
Mastronardi, Nicola; Van Barel, Marc; Vandebril, Raf A note on the recursive calculation of dominant singular subspaces. (English) Zbl 1068.65054 Numer. Algorithms 38, No. 4, 237-242 (2005). MSC: 65F30 65F20 65F25 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., Numer. Algorithms 38, No. 4, 237--242 (2005; Zbl 1068.65054) Full Text: DOI Link
Vandebril, Raf; Van Barel, Marc; Mastronardi, Nicola A QR-method for computing the singular values via semiseparable matrices. (English) Zbl 1069.65044 Numer. Math. 99, No. 1, 163-195 (2004). Reviewer: Michael Jung (Dresden) MSC: 65F20 65F15 PDFBibTeX XMLCite \textit{R. Vandebril} et al., Numer. Math. 99, No. 1, 163--195 (2004; Zbl 1069.65044) Full Text: DOI
Hendrickx, Jef; Vandebril, Raf; Van Barel, Marc A fast direct method for solving the two-dimensional Helmholtz equation, with Robbins boundary conditions. (English) Zbl 1044.65077 Olshevsky, Vadim (ed.), Fast algorithms for structured matrices: Theory and applications. AMS-IMS-SIAM joint summer research conference on fast algorithms in mathematics, computer science and engineering, August 5–9, 2001, South Hadley, Massachusetts. Providence, RI: American Mathematical Society (AMS); Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 0-8218-3177-1/pbk; 0-89871-543-1/pbk). Contemp. Math. 323, 187-204 (2003). MSC: 65N06 65N12 35J05 65Y20 PDFBibTeX XMLCite \textit{J. Hendrickx} et al., Contemp. Math. 323, 187--204 (2003; Zbl 1044.65077)