Amparan, Agurtzane; Baragaña, Itziar; Marcaida, Silvia; Roca, Alicia Row or column completion of polynomial matrices of given degree. (English) Zbl 07805917 SIAM J. Matrix Anal. Appl. 45, No. 1, 478-503 (2024). MSC: 15A18 15A21 15A83 PDFBibTeX XMLCite \textit{A. Amparan} et al., SIAM J. Matrix Anal. Appl. 45, No. 1, 478--503 (2024; Zbl 07805917) Full Text: DOI arXiv
Dopico, Froilán M.; Noferini, Vanni The \(\mathbb{DL}(P)\) vector space of pencils for singular matrix polynomials. (English) Zbl 1525.65028 Linear Algebra Appl. 677, 88-131 (2023). MSC: 65F15 15A18 15A22 15A54 PDFBibTeX XMLCite \textit{F. M. Dopico} and \textit{V. Noferini}, Linear Algebra Appl. 677, 88--131 (2023; Zbl 1525.65028) Full Text: DOI arXiv
Noferini, Vanni; Nyman, Lauri; Pérez, Javier; Quintana, María C. Perturbation theory of transfer function matrices. (English) Zbl 1522.65052 SIAM J. Matrix Anal. Appl. 44, No. 3, 1299-1320 (2023). MSC: 65F15 15A18 15A54 93B20 93B60 PDFBibTeX XMLCite \textit{V. Noferini} et al., SIAM J. Matrix Anal. Appl. 44, No. 3, 1299--1320 (2023; Zbl 1522.65052) Full Text: DOI arXiv
Melman, A. Matrices whose eigenvalues are those of a quadratic matrix polynomial. (English) Zbl 1523.15008 Linear Algebra Appl. 676, 131-149 (2023). Reviewer: Roksana Słowik (Gliwice) MSC: 15A18 15A42 PDFBibTeX XMLCite \textit{A. Melman}, Linear Algebra Appl. 676, 131--149 (2023; Zbl 1523.15008) Full Text: DOI
Garvey, Seamus D.; Tisseur, Françoise; Wang, Shujuan A parametrization of structure-preserving transformations for matrix polynomials. (English) Zbl 1518.65046 Linear Algebra Appl. 674, 68-90 (2023). MSC: 65F60 15A22 15A18 47J10 PDFBibTeX XMLCite \textit{S. D. Garvey} et al., Linear Algebra Appl. 674, 68--90 (2023; Zbl 1518.65046) Full Text: DOI
Szymański, Oskar Jakub; Wojtylak, Michał Stability of matrix polynomials in one and several variables. (English) Zbl 1515.15012 Linear Algebra Appl. 670, 42-67 (2023). Reviewer: Roksana Słowik (Gliwice) MSC: 15A18 15A22 15B57 30C15 32A60 PDFBibTeX XMLCite \textit{O. J. Szymański} and \textit{M. Wojtylak}, Linear Algebra Appl. 670, 42--67 (2023; Zbl 1515.15012) Full Text: DOI arXiv
Perović, Vasilije; Mackey, D. Steven Quadratic realizability of palindromic matrix polynomials: the real case. (English) Zbl 1519.15017 Linear Multilinear Algebra 71, No. 5, 797-841 (2023). Reviewer: Ninoslav Truhar (Osijek) MSC: 15A29 15A21 15A22 PDFBibTeX XMLCite \textit{V. Perović} and \textit{D. S. Mackey}, Linear Multilinear Algebra 71, No. 5, 797--841 (2023; Zbl 1519.15017) Full Text: DOI
Mele, Giampaolo The infinite Lanczos method for symmetric nonlinear eigenvalue problems. (English) Zbl 07668048 Calcolo 60, No. 2, Paper No. 19, 24 p. (2023). MSC: 47J10 35P30 65H17 65F60 15A18 65F15 PDFBibTeX XMLCite \textit{G. Mele}, Calcolo 60, No. 2, Paper No. 19, 24 p. (2023; Zbl 07668048) Full Text: DOI arXiv
Koval, Vadym; Pagacz, Patryk Matrix pencils with the numerical range equal to the whole complex plane. (English) Zbl 1503.15009 Linear Algebra Appl. 657, 274-286 (2023). Reviewer: Ioannis Dassios (Dublin) MSC: 15A22 15A60 PDFBibTeX XMLCite \textit{V. Koval} and \textit{P. Pagacz}, Linear Algebra Appl. 657, 274--286 (2023; Zbl 1503.15009) Full Text: DOI arXiv
Melman, Aaron Polynomial eigenvalue estimation: numerical radii versus norms. (English) Zbl 1514.15026 Linear Multilinear Algebra 70, No. 22, 7656-7671 (2022). MSC: 15A42 15A18 47A12 PDFBibTeX XMLCite \textit{A. Melman}, Linear Multilinear Algebra 70, No. 22, 7656--7671 (2022; Zbl 1514.15026) Full Text: DOI
Dopico, Froilán M.; Quintana, María C.; Van Dooren, Paul Strongly minimal self-conjugate linearizations for polynomial and rational matrices. (English) Zbl 1506.15013 SIAM J. Matrix Anal. Appl. 43, No. 3, 1354-1381 (2022). MSC: 15A21 15A18 15A22 15A54 15B57 PDFBibTeX XMLCite \textit{F. M. Dopico} et al., SIAM J. Matrix Anal. Appl. 43, No. 3, 1354--1381 (2022; Zbl 1506.15013) Full Text: DOI arXiv
Pagacz, Patryk; Wojtylak, Michał Random perturbations of matrix polynomials. (English) Zbl 1491.15042 J. Theor. Probab. 35, No. 1, 52-88 (2022). Reviewer: Sen Zhu (Changchun) MSC: 15B52 60B20 47A55 PDFBibTeX XMLCite \textit{P. Pagacz} and \textit{M. Wojtylak}, J. Theor. Probab. 35, No. 1, 52--88 (2022; Zbl 1491.15042) Full Text: DOI arXiv
Dmytryshyn, Andrii Recovering a perturbation of a matrix polynomial from a perturbation of its first companion linearization. (English) Zbl 1485.65052 BIT 62, No. 1, 69-88 (2022). MSC: 65F99 15A22 15A21 65F15 65F35 PDFBibTeX XMLCite \textit{A. Dmytryshyn}, BIT 62, No. 1, 69--88 (2022; Zbl 1485.65052) Full Text: DOI arXiv
Bevilacqua, R.; Del Corso, G. M.; Gemignani, L. Orthogonal iterations on companion-like pencils. (English) Zbl 1487.65040 J. Sci. Comput. 91, No. 1, Paper No. 6, 22 p. (2022). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{R. Bevilacqua} et al., J. Sci. Comput. 91, No. 1, Paper No. 6, 22 p. (2022; Zbl 1487.65040) Full Text: DOI
Cao, Zongqi; Wang, Xiang; Chen, Hongjia On the conditioning for heavily damped quadratic eigenvalue problem solved by linearizations. (English) Zbl 1481.15006 Japan J. Ind. Appl. Math. 39, No. 1, 419-441 (2022). MSC: 15A18 15A22 65F15 PDFBibTeX XMLCite \textit{Z. Cao} et al., Japan J. Ind. Appl. Math. 39, No. 1, 419--441 (2022; Zbl 1481.15006) Full Text: DOI
Chan, Eunice Y. S.; Corless, Robert M.; Sevyeri, Leili Rafiee Generalized standard triples for algebraic linearizations of matrix polynomials. (English) Zbl 1490.15020 Electron. J. Linear Algebra 37, 640-658 (2021). MSC: 15A22 65F15 65D05 PDFBibTeX XMLCite \textit{E. Y. S. Chan} et al., Electron. J. Linear Algebra 37, 640--658 (2021; Zbl 1490.15020) Full Text: arXiv Link
Chen, Hongjia; Du, Lei; Cao, Zongqi Backward error analysis of linearizing-balancing strategies for heavily damped quadratic eigenvalue problem. (English) Zbl 1524.65163 Appl. Math. Lett. 120, Article ID 107342, 6 p. (2021). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{H. Chen} et al., Appl. Math. Lett. 120, Article ID 107342, 6 p. (2021; Zbl 1524.65163) Full Text: DOI
Chen, Hongjia; Xu, Kuan On the backward error incurred by the compact rational Krylov linearization. (English) Zbl 1473.65045 J. Sci. Comput. 89, No. 1, Paper No. 15, 22 p. (2021). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{H. Chen} and \textit{K. Xu}, J. Sci. Comput. 89, No. 1, Paper No. 15, 22 p. (2021; Zbl 1473.65045) Full Text: DOI
Benner, Peter; Fassbender, Heike; Saltenberger, Philip A rational even-IRA algorithm for the solution of \(T\)-even polynomial eigenvalue problems. (English) Zbl 1528.65021 SIAM J. Matrix Anal. Appl. 42, No. 3, 1172-1198 (2021). MSC: 65F15 65F99 15A18 15A54 15B57 PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM J. Matrix Anal. Appl. 42, No. 3, 1172--1198 (2021; Zbl 1528.65021) Full Text: DOI arXiv
Ringh, Emil; Jarlebring, Elias Nonlinearizing two-parameter eigenvalue problems. (English) Zbl 07365300 SIAM J. Matrix Anal. Appl. 42, No. 2, 775-799 (2021). MSC: 65F15 15A18 47J10 65H17 15A22 15A69 PDFBibTeX XMLCite \textit{E. Ringh} and \textit{E. Jarlebring}, SIAM J. Matrix Anal. Appl. 42, No. 2, 775--799 (2021; Zbl 07365300) Full Text: DOI arXiv
Tisseur, Françoise; Van Barel, Marc Min-max elementwise backward error for roots of polynomials and a corresponding backward stable root finder. (English) Zbl 1470.65094 Linear Algebra Appl. 623, 454-477 (2021). MSC: 65H04 65F15 30C15 15A22 15A80 15A18 47J10 PDFBibTeX XMLCite \textit{F. Tisseur} and \textit{M. Van Barel}, Linear Algebra Appl. 623, 454--477 (2021; Zbl 1470.65094) Full Text: DOI arXiv
De Terán, Fernando; Hernando, Carla; Pérez, Javier Structured strong \(\ell \)-ifications for structured matrix polynomials in the monomial basis. (English) Zbl 1475.15016 Electron. J. Linear Algebra 37, 35-71 (2021). Reviewer: Mihail Voicu (Iaşi) MSC: 15A22 15A18 15A16 15A21 15B57 65F15 PDFBibTeX XMLCite \textit{F. De Terán} et al., Electron. J. Linear Algebra 37, 35--71 (2021; Zbl 1475.15016) Full Text: arXiv Link
Benner, Peter; Liang, Xin; Miodragović, Suzana; Truhar, Ninoslav Relative perturbation theory for quadratic Hermitian eigenvalue problems. (English) Zbl 1470.65059 Linear Algebra Appl. 618, 97-128 (2021). MSC: 65F15 15A22 15B57 15A24 47A55 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 618, 97--128 (2021; Zbl 1470.65059) Full Text: DOI arXiv
Amparan, A.; Marcaida, S.; Zaballa, I. Spectral filters connecting high order systems. (English) Zbl 1488.37017 Appl. Math. Comput. 391, Article ID 125672, 15 p. (2021). MSC: 37C30 15A22 15A18 PDFBibTeX XMLCite \textit{A. Amparan} et al., Appl. Math. Comput. 391, Article ID 125672, 15 p. (2021; Zbl 1488.37017) Full Text: DOI
Drmač, Zlatko; Glibić, Ivana Šain New numerical algorithm for deflation of infinite and zero eigenvalues and full solution of quadratic eigenvalue problems. (English) Zbl 1486.65051 ACM Trans. Math. Softw. 46, No. 4, Article No. 30, 32 p. (2020). MSC: 65H17 65F15 15A22 PDFBibTeX XMLCite \textit{Z. Drmač} and \textit{I. Š. Glibić}, ACM Trans. Math. Softw. 46, No. 4, Article No. 30, 32 p. (2020; Zbl 1486.65051) Full Text: DOI arXiv
De Terán, Fernando; Dmytryshyn, Andrii; Dopico, Froilán M. Generic symmetric matrix polynomials with bounded rank and fixed odd grade. (English) Zbl 1458.15015 SIAM J. Matrix Anal. Appl. 41, No. 3, 1033-1058 (2020). Reviewer: Tin Yau Tam (Reno) MSC: 15A18 15A03 15A21 15A22 47A56 65F15 PDFBibTeX XMLCite \textit{F. De Terán} et al., SIAM J. Matrix Anal. Appl. 41, No. 3, 1033--1058 (2020; Zbl 1458.15015) Full Text: DOI arXiv
Dmytryshyn, Andrii; Johansson, Stefan; Kågström, Bo; Van Dooren, Paul Geometry of matrix polynomial spaces. (English) Zbl 1444.15007 Found. Comput. Math. 20, No. 3, 423-450 (2020). Reviewer: Tin Yau Tam (Reno) MSC: 15A21 15A22 47A07 PDFBibTeX XMLCite \textit{A. Dmytryshyn} et al., Found. Comput. Math. 20, No. 3, 423--450 (2020; Zbl 1444.15007) Full Text: DOI
Campos, Carmen; Roman, Jose E. A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation. (English) Zbl 1442.65054 BIT 60, No. 2, 295-318 (2020). Reviewer: Wei-Ru Xu (Chengdu) MSC: 65F15 15A18 65F50 PDFBibTeX XMLCite \textit{C. Campos} and \textit{J. E. Roman}, BIT 60, No. 2, 295--318 (2020; Zbl 1442.65054) Full Text: DOI
Chen, Hongjia; Du, Lei Backward error bounds for polynomial eigenvalue problem solved by a Rayleigh-Ritz type contour integral-based eigensolver. (English) Zbl 1524.65162 Appl. Math. Lett. 102, Article ID 106122, 6 p. (2020). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{H. Chen} and \textit{L. Du}, Appl. Math. Lett. 102, Article ID 106122, 6 p. (2020; Zbl 1524.65162) Full Text: DOI
Malyshev, Alexander; Sadkane, Miloud Computing the distance to continuous-time instability of quadratic matrix polynomials. (English) Zbl 1440.65049 Numer. Math. 145, No. 1, 149-165 (2020). MSC: 65F15 15A22 65F35 65G50 PDFBibTeX XMLCite \textit{A. Malyshev} and \textit{M. Sadkane}, Numer. Math. 145, No. 1, 149--165 (2020; Zbl 1440.65049) Full Text: DOI Link
Hochstenbach, Michiel E.; Plestenjak, Bor Computing several eigenvalues of nonlinear eigenvalue problems by selection. (English) Zbl 1439.65045 Calcolo 57, No. 2, Paper No. 16, 25 p. (2020). Reviewer: Anton Iliev (Plovdiv) MSC: 65F15 65F50 65H17 15A18 15A69 PDFBibTeX XMLCite \textit{M. E. Hochstenbach} and \textit{B. Plestenjak}, Calcolo 57, No. 2, Paper No. 16, 25 p. (2020; Zbl 1439.65045) Full Text: DOI arXiv
De Terán, Fernando Backward error and conditioning of Fiedler companion linearizations. (English) Zbl 1433.65050 Math. Comput. 89, No. 323, 1259-1300 (2020). MSC: 65F15 65F18 15A18 65F35 PDFBibTeX XMLCite \textit{F. De Terán}, Math. Comput. 89, No. 323, 1259--1300 (2020; Zbl 1433.65050) Full Text: DOI
Pandur, Marija Miloloža Detecting a hyperbolic quadratic eigenvalue problem by using a subspace algorithm. (English) Zbl 1434.65037 Numer. Algorithms 83, No. 2, 767-787 (2020). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 65F15 65F18 15A18 65H17 65Y15 PDFBibTeX XMLCite \textit{M. M. Pandur}, Numer. Algorithms 83, No. 2, 767--787 (2020; Zbl 1434.65037) Full Text: DOI
Anguas, Luis Miguel; Bueno, Maria Isabel; Dopico, Froilán M. Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations. (English) Zbl 1427.65045 Math. Comput. 89, No. 322, 767-805 (2020). MSC: 65F15 65F35 15A18 15A22 PDFBibTeX XMLCite \textit{L. M. Anguas} et al., Math. Comput. 89, No. 322, 767--805 (2020; Zbl 1427.65045) Full Text: DOI arXiv
Melman, A. Directional bounds for polynomial zeros and eigenvalues. (English) Zbl 1430.30002 J. Math. Anal. Appl. 482, No. 2, Article ID 123571, 11 p. (2020). MSC: 30C10 30C15 15A18 15A42 PDFBibTeX XMLCite \textit{A. Melman}, J. Math. Anal. Appl. 482, No. 2, Article ID 123571, 11 p. (2020; Zbl 1430.30002) Full Text: DOI
Alam, Rafikul; Safique Ahmad, Sk. Sensitivity analysis of nonlinear eigenproblems. (English) Zbl 1420.65042 SIAM J. Matrix Anal. Appl. 40, No. 2, 672-695 (2019). MSC: 65F15 15A12 15A18 65F35 PDFBibTeX XMLCite \textit{R. Alam} and \textit{Sk. Safique Ahmad}, SIAM J. Matrix Anal. Appl. 40, No. 2, 672--695 (2019; Zbl 1420.65042) Full Text: DOI
Nakatsukasa, Yuji; Noferini, Vanni Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems. (English) Zbl 1420.15010 Linear Algebra Appl. 578, 272-296 (2019). Reviewer: Wei-Ru Xu (Chengdu) MSC: 15A18 15A22 65F15 15B57 PDFBibTeX XMLCite \textit{Y. Nakatsukasa} and \textit{V. Noferini}, Linear Algebra Appl. 578, 272--296 (2019; Zbl 1420.15010) Full Text: DOI arXiv
Seeger, Alberto Cone-constrained rational eigenvalue problems. (English) Zbl 1419.15009 Electron. J. Linear Algebra 35, 187-203 (2019). Reviewer: Anton Iliev (Plovdiv) MSC: 15A18 15A22 15A39 65H17 PDFBibTeX XMLCite \textit{A. Seeger}, Electron. J. Linear Algebra 35, 187--203 (2019; Zbl 1419.15009) Full Text: DOI
Melman, A. Polynomial eigenvalue bounds from companion matrix polynomials. (English) Zbl 1407.15012 Linear Multilinear Algebra 67, No. 3, 598-612 (2019). MSC: 15A18 47A46 65F15 PDFBibTeX XMLCite \textit{A. Melman}, Linear Multilinear Algebra 67, No. 3, 598--612 (2019; Zbl 1407.15012) Full Text: DOI
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
Kostić, V.; Gardašević, D. On the Geršgorin-type localizations for nonlinear eigenvalue problems. (English) Zbl 1427.65049 Appl. Math. Comput. 337, 179-189 (2018). MSC: 65F15 15A24 15A42 PDFBibTeX XMLCite \textit{V. Kostić} and \textit{D. Gardašević}, Appl. Math. Comput. 337, 179--189 (2018; Zbl 1427.65049) Full Text: DOI
Ringh, Emil; Mele, Giampaolo; Karlsson, Johan; Jarlebring, Elias Sylvester-based preconditioning for the waveguide eigenvalue problem. (English) Zbl 1418.65050 Linear Algebra Appl. 542, 441-463 (2018). MSC: 65F15 65F08 65F10 65F30 15A24 35P30 PDFBibTeX XMLCite \textit{E. Ringh} et al., Linear Algebra Appl. 542, 441--463 (2018; Zbl 1418.65050) Full Text: DOI arXiv
Van Barel, Marc; Tisseur, Françoise Polynomial eigenvalue solver based on tropically scaled Lagrange linearization. (English) Zbl 1418.65052 Linear Algebra Appl. 542, 186-208 (2018). MSC: 65F15 15A22 15A80 15A18 47J10 PDFBibTeX XMLCite \textit{M. Van Barel} and \textit{F. Tisseur}, Linear Algebra Appl. 542, 186--208 (2018; Zbl 1418.65052) Full Text: DOI Link
Lietaert, Pieter; Meerbergen, Karl; Tisseur, Françoise Compact two-sided Krylov methods for nonlinear eigenvalue problems. (English) Zbl 1397.65056 SIAM J. Sci. Comput. 40, No. 5, A2801-A2829 (2018). MSC: 65F15 65F25 15A18 15A22 41A20 47J10 PDFBibTeX XMLCite \textit{P. Lietaert} et al., SIAM J. Sci. Comput. 40, No. 5, A2801--A2829 (2018; Zbl 1397.65056) Full Text: DOI
Zhao, Tao A convergence analysis of the inexact simplified Jacobi-Davidson algorithm for polynomial eigenvalue problems. (English) Zbl 1415.65120 J. Sci. Comput. 75, No. 3, 1207-1228 (2018). MSC: 65H17 65F15 15A22 PDFBibTeX XMLCite \textit{T. Zhao}, J. Sci. Comput. 75, No. 3, 1207--1228 (2018; Zbl 1415.65120) Full Text: DOI
Xue, Fei A block preconditioned harmonic projection method for large-scale nonlinear eigenvalue problems. (English) Zbl 1391.65092 SIAM J. Sci. Comput. 40, No. 3, A1809-A1835 (2018). MSC: 65F15 65F50 15A18 15A22 PDFBibTeX XMLCite \textit{F. Xue}, SIAM J. Sci. Comput. 40, No. 3, A1809--A1835 (2018; Zbl 1391.65092) Full Text: DOI
Melman, A. Eigenvalue bounds for matrix polynomials in generalized bases. (English) Zbl 1392.15020 Math. Comput. 87, No. 312, 1935-1948 (2018). Reviewer: Iveta Hnetynkova (Praha) MSC: 15A18 47A56 65F15 PDFBibTeX XMLCite \textit{A. Melman}, Math. Comput. 87, No. 312, 1935--1948 (2018; Zbl 1392.15020) Full Text: DOI arXiv
Mele, Giampaolo; Jarlebring, Elias On restarting the tensor infinite Arnoldi method. (English) Zbl 1386.65132 BIT 58, No. 1, 133-162 (2018). MSC: 65F60 35P30 65H17 15A18 65F15 PDFBibTeX XMLCite \textit{G. Mele} and \textit{E. Jarlebring}, BIT 58, No. 1, 133--162 (2018; Zbl 1386.65132) Full Text: DOI arXiv
Boito, P.; Eidelman, Y.; Gemignani, L. A real QZ algorithm for structured companion pencils. (English) Zbl 1382.65097 Calcolo 54, No. 4, 1305-1338 (2017). MSC: 65F15 65H04 15A22 PDFBibTeX XMLCite \textit{P. Boito} et al., Calcolo 54, No. 4, 1305--1338 (2017; Zbl 1382.65097) Full Text: DOI arXiv
Dmytryshyn, Andrii Structure preserving stratification of skew-symmetric matrix polynomials. (English) Zbl 1370.15008 Linear Algebra Appl. 532, 266-286 (2017). MSC: 15A21 15A22 65F15 47A07 PDFBibTeX XMLCite \textit{A. Dmytryshyn}, Linear Algebra Appl. 532, 266--286 (2017; Zbl 1370.15008) Full Text: DOI Link
Xiao, Jinyou; Zhou, Hang; Zhang, Chuanzeng; Xu, Chao Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method. (English) Zbl 1398.65066 Comput. Mech. 59, No. 2, 317-334 (2017). MSC: 65F15 65H17 65F35 15A18 65F10 PDFBibTeX XMLCite \textit{J. Xiao} et al., Comput. Mech. 59, No. 2, 317--334 (2017; Zbl 1398.65066) Full Text: DOI
Wang, Xiang; Tang, Xiao-Bin; Mao, Liang-Zhi A modified second-order Arnoldi method for solving the quadratic eigenvalue problems. (English) Zbl 1368.65059 Comput. Math. Appl. 73, No. 2, 327-338 (2017). MSC: 65F15 65H17 15A24 PDFBibTeX XMLCite \textit{X. Wang} et al., Comput. Math. Appl. 73, No. 2, 327--338 (2017; Zbl 1368.65059) Full Text: DOI
Barkatou, Moulay; Boito, Paola; Segura Ugalde, Esteban A contour integral approach to the computation of invariant pairs. (English) Zbl 1375.65057 Theor. Comput. Sci. 681, 3-26 (2017). MSC: 65F15 15A54 PDFBibTeX XMLCite \textit{M. Barkatou} et al., Theor. Comput. Sci. 681, 3--26 (2017; Zbl 1375.65057) Full Text: DOI arXiv
Campos, Carmen; Roman, Jose E. Parallel Krylov solvers for the polynomial eigenvalue problem in SLEPc. (English) Zbl 1352.65116 SIAM J. Sci. Comput. 38, No. 5, S385-S411 (2016). MSC: 65F15 65F50 65Y05 15A54 PDFBibTeX XMLCite \textit{C. Campos} and \textit{J. E. Roman}, SIAM J. Sci. Comput. 38, No. 5, S385--S411 (2016; Zbl 1352.65116) Full Text: DOI
Melman, A. Bounds for eigenvalues of matrix polynomials with applications to scalar polynomials. (English) Zbl 1338.15028 Linear Algebra Appl. 504, 190-203 (2016). MSC: 15A18 30C15 65F15 PDFBibTeX XMLCite \textit{A. Melman}, Linear Algebra Appl. 504, 190--203 (2016; Zbl 1338.15028) Full Text: DOI
Bini, Dario A.; Robol, Leonardo On a class of matrix pencils and \(\ell\)-ifications equivalent to a given matrix polynomial. (English) Zbl 1338.65099 Linear Algebra Appl. 502, 275-298 (2016). MSC: 65F15 15A21 15A03 PDFBibTeX XMLCite \textit{D. A. Bini} and \textit{L. Robol}, Linear Algebra Appl. 502, 275--298 (2016; Zbl 1338.65099) Full Text: DOI arXiv
Alam, Rafikul; Behera, Namita Linearizations for rational matrix functions and Rosenbrock system polynomials. (English) Zbl 1376.65042 SIAM J. Matrix Anal. Appl. 37, No. 1, 354-380 (2016). MSC: 65F15 15A18 65F35 15B57 PDFBibTeX XMLCite \textit{R. Alam} and \textit{N. Behera}, SIAM J. Matrix Anal. Appl. 37, No. 1, 354--380 (2016; Zbl 1376.65042) Full Text: DOI
Bindel, David; Hood, Amanda Localization theorems for nonlinear eigenvalue problems. (English) Zbl 1338.15022 SIAM Rev. 57, No. 4, 585-607 (2015). MSC: 15A18 15A42 15A60 30E10 PDFBibTeX XMLCite \textit{D. Bindel} and \textit{A. Hood}, SIAM Rev. 57, No. 4, 585--607 (2015; Zbl 1338.15022) Full Text: DOI
Benner, Peter; Losse, Philip; Mehrmann, Volker; Voigt, Matthias Numerical linear algebra methods for linear differential-algebraic equations. (English) Zbl 1343.65100 Ilchmann, Achim (ed.) et al., Surveys in differential-algebraic equations III. Cham: Springer (ISBN 978-3-319-22427-5/pbk; 978-3-319-22428-2/ebook). Differential-Algebraic Equations Forum, 117-175 (2015). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 65L80 15A21 15A22 34A09 65F15 93C05 93D09 65K10 93B05 93C15 93B36 93-02 65-02 49N10 PDFBibTeX XMLCite \textit{P. Benner} et al., in: Surveys in differential-algebraic equations III. Cham: Springer. 117--175 (2015; Zbl 1343.65100) Full Text: DOI
Truhar, Ninoslav; Miodragović, Suzana Relative perturbation theory for definite matrix pairs and hyperbolic eigenvalue problem. (English) Zbl 1329.15072 Appl. Numer. Math. 98, 106-121 (2015). MSC: 15B57 15A42 65F15 65F35 PDFBibTeX XMLCite \textit{N. Truhar} and \textit{S. Miodragović}, Appl. Numer. Math. 98, 106--121 (2015; Zbl 1329.15072) Full Text: DOI
Lawrence, Piers W.; Corless, Robert M. Backward error of polynomial eigenvalue problems solved by linearization of Lagrange interpolants. (English) Zbl 1327.65073 SIAM J. Matrix Anal. Appl. 36, No. 4, 1425-1442 (2015). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{P. W. Lawrence} and \textit{R. M. Corless}, SIAM J. Matrix Anal. Appl. 36, No. 4, 1425--1442 (2015; Zbl 1327.65073) Full Text: DOI Link
Van Beeumen, Roel; Meerbergen, Karl; Michiels, Wim Compact rational Krylov methods for nonlinear eigenvalue problems. (English) Zbl 1319.65042 SIAM J. Matrix Anal. Appl. 36, No. 2, 820-838 (2015). MSC: 65H17 65F15 15A22 65F25 PDFBibTeX XMLCite \textit{R. Van Beeumen} et al., SIAM J. Matrix Anal. Appl. 36, No. 2, 820--838 (2015; Zbl 1319.65042) Full Text: DOI Link
Taslaman, Leo Strongly damped quadratic matrix polynomials. (English) Zbl 1320.15007 SIAM J. Matrix Anal. Appl. 36, No. 2, 461-475 (2015). MSC: 15A18 15A22 15A54 65F15 70J10 70J30 70J50 PDFBibTeX XMLCite \textit{L. Taslaman}, SIAM J. Matrix Anal. Appl. 36, No. 2, 461--475 (2015; Zbl 1320.15007) Full Text: DOI
Noferini, Vanni; Sharify, Meisam; Tisseur, Françoise Tropical roots as approximations to eigenvalues of matrix polynomials. (English) Zbl 1315.65038 SIAM J. Matrix Anal. Appl. 36, No. 1, 138-157 (2015). MSC: 65F15 15A22 15A80 15A12 65F35 PDFBibTeX XMLCite \textit{V. Noferini} et al., SIAM J. Matrix Anal. Appl. 36, No. 1, 138--157 (2015; Zbl 1315.65038) Full Text: DOI
Noferini, Vanni; Poloni, Federico Duality of matrix pencils, Wong chains and linearizations. (English) Zbl 1308.15009 Linear Algebra Appl. 471, 730-767 (2015). MSC: 15A18 15A22 PDFBibTeX XMLCite \textit{V. Noferini} and \textit{F. Poloni}, Linear Algebra Appl. 471, 730--767 (2015; Zbl 1308.15009) Full Text: DOI
Kressner, Daniel; Roman, Jose E. Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis. (English) Zbl 1340.65059 Numer. Linear Algebra Appl. 21, No. 4, 569-588 (2014). Reviewer: Karl Meerbergen (Leuven) MSC: 65F15 15A18 15A22 65H17 PDFBibTeX XMLCite \textit{D. Kressner} and \textit{J. E. Roman}, Numer. Linear Algebra Appl. 21, No. 4, 569--588 (2014; Zbl 1340.65059) Full Text: DOI Link
Kressner, Daniel; Pandur, Marija Miloloža; Shao, Meiyue An indefinite variant of LOBPCG for definite matrix pencils. (English) Zbl 1297.65040 Numer. Algorithms 66, No. 4, 681-703 (2014). MSC: 65F15 65F08 15A22 PDFBibTeX XMLCite \textit{D. Kressner} et al., Numer. Algorithms 66, No. 4, 681--703 (2014; Zbl 1297.65040) Full Text: DOI Link
Bini, Dario A.; Noferini, Vanni Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method. (English) Zbl 1281.65061 Linear Algebra Appl. 439, No. 4, 1130-1149 (2013). MSC: 65F15 15A16 15A54 PDFBibTeX XMLCite \textit{D. A. Bini} and \textit{V. Noferini}, Linear Algebra Appl. 439, No. 4, 1130--1149 (2013; Zbl 1281.65061) Full Text: DOI arXiv
De Terán, Fernando; Dopico, Froilán M.; Mackey, D. Steven Fiedler companion linearizations for rectangular matrix polynomials. (English) Zbl 1259.15031 Linear Algebra Appl. 437, No. 3, 957-991 (2012). Reviewer: Edgar Pereira (Natal) MSC: 15A54 65F15 15A18 15A22 47H60 PDFBibTeX XMLCite \textit{F. De Terán} et al., Linear Algebra Appl. 437, No. 3, 957--991 (2012; Zbl 1259.15031) Full Text: DOI
Ahmad, Sk. Safique; Mehrmann, Volker Perturbation analysis for complex symmetric, skew symmetric, even and odd matrix polynomials. (English) Zbl 1321.65053 ETNA, Electron. Trans. Numer. Anal. 38, 275-302 (2011). MSC: 65F15 15A18 65F35 15A12 PDFBibTeX XMLCite \textit{Sk. S. Ahmad} and \textit{V. Mehrmann}, ETNA, Electron. Trans. Numer. Anal. 38, 275--302 (2011; Zbl 1321.65053) Full Text: EMIS
Su, Yangfeng; Bai, Zhaojun Solving rational eigenvalue problems via linearization. (English) Zbl 1222.65034 SIAM J. Matrix Anal. Appl. 32, No. 1, 201-216 (2011). Reviewer: Alan L. Andrew (Bundoora) MSC: 65F15 65F50 15A22 47A56 PDFBibTeX XMLCite \textit{Y. Su} and \textit{Z. Bai}, SIAM J. Matrix Anal. Appl. 32, No. 1, 201--216 (2011; Zbl 1222.65034) Full Text: DOI
Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise A framework for analyzing nonlinear eigenproblems and parametrized linear systems. (English) Zbl 1288.65049 Linear Algebra Appl. 435, No. 3, 623-640 (2011). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{L. Grammont} et al., Linear Algebra Appl. 435, No. 3, 623--640 (2011; Zbl 1288.65049) Full Text: DOI Link
Betcke, Timo; Kressner, Daniel Perturbation, extraction and refinement of invariant pairs for matrix polynomials. (English) Zbl 1228.15008 Linear Algebra Appl. 435, No. 3, 514-536 (2011). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15A54 15A18 65F15 PDFBibTeX XMLCite \textit{T. Betcke} and \textit{D. Kressner}, Linear Algebra Appl. 435, No. 3, 514--536 (2011; Zbl 1228.15008) Full Text: DOI
Tisseur, Françoise; Garvey, Seamus D.; Munro, Christopher Deflating quadratic matrix polynomials with structure preserving transformations. (English) Zbl 1235.15010 Linear Algebra Appl. 435, No. 3, 464-479 (2011). Reviewer: Tin Yau Tam (Auburn) MSC: 15A18 65F15 65F30 15A86 15A54 PDFBibTeX XMLCite \textit{F. Tisseur} et al., Linear Algebra Appl. 435, No. 3, 464--479 (2011; Zbl 1235.15010) Full Text: DOI Link
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise An improved arc algorithm for detecting definite Hermitian pairs. (English) Zbl 1202.65054 SIAM J. Matrix Anal. Appl. 31(2009), No. 3, 1131-1151 (2010). Reviewer: Georg Hebermehl (Berlin) MSC: 65F30 65F15 15A18 15B57 PDFBibTeX XMLCite \textit{C.-H. Guo} et al., SIAM J. Matrix Anal. Appl. 31, No. 3, 1131--1151 (2010; Zbl 1202.65054) Full Text: DOI