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
Dong, Bo The homotopy method for the complete solution of quadratic two-parameter eigenvalue problems. (English) Zbl 1483.65059 J. Sci. Comput. 90, No. 1, Paper No. 18, 25 p. (2022). MSC: 65F15 15A22 15A69 15A18 34K20 PDFBibTeX XMLCite \textit{B. Dong}, J. Sci. Comput. 90, No. 1, Paper No. 18, 25 p. (2022; Zbl 1483.65059) Full Text: DOI
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
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
Beltrán, Carlos; Kozhasov, Khazhgali The real polynomial eigenvalue problem is well conditioned on the average. (English) Zbl 1472.14068 Found. Comput. Math. 20, No. 2, 291-309 (2020). Reviewer: Jana Chalmovianská (Bratislava) MSC: 14Q20 15A18 15A22 15B52 65F15 PDFBibTeX XMLCite \textit{C. Beltrán} and \textit{K. Kozhasov}, Found. Comput. Math. 20, No. 2, 291--309 (2020; Zbl 1472.14068) 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
Lê, Công-Trình; Du, Thi-Hoa-binh; Nguyen, Tran-Duc On the location of eigenvalues of matrix polynomials. (English) Zbl 1432.15008 Oper. Matrices 13, No. 4, 937-954 (2019). MSC: 15A18 15A42 65F15 PDFBibTeX XMLCite \textit{C.-T. Lê} et al., Oper. Matrices 13, No. 4, 937--954 (2019; Zbl 1432.15008) Full Text: DOI arXiv
Anguas, Luis M.; Dopico, FroiláN M.; Hollister, Richard; Mackey, D. Steven Van Dooren’s index sum theorem and rational matrices with prescribed structural data. (English) Zbl 1428.15016 SIAM J. Matrix Anal. Appl. 40, No. 2, 720-738 (2019). Reviewer: Juan Ramon Torregrosa Sanchez (Valencia) MSC: 15A29 65F18 93B55 93B60 PDFBibTeX XMLCite \textit{L. M. Anguas} et al., SIAM J. Matrix Anal. Appl. 40, No. 2, 720--738 (2019; Zbl 1428.15016) Full Text: DOI
Malyshev, Alexander; Sadkane, Miloud On the distance to instability of quadratic matrix polynomials. (Sur la distance à l’instabilité de polynômes matriciels quadratiques.) (French. Abridged English version) Zbl 1417.15041 C. R., Math., Acad. Sci. Paris 357, No. 6, 571-575 (2019). MSC: 15A99 15B05 PDFBibTeX XMLCite \textit{A. Malyshev} and \textit{M. Sadkane}, C. R., Math., Acad. Sci. Paris 357, No. 6, 571--575 (2019; Zbl 1417.15041) Full Text: DOI
Anguas, Luis Miguel; Bueno, María Isabel; Dopico, Froilán M. A comparison of eigenvalue condition numbers for matrix polynomials. (English) Zbl 1407.15010 Linear Algebra Appl. 564, 170-200 (2019). MSC: 15A18 15A22 65F15 65F35 PDFBibTeX XMLCite \textit{L. M. Anguas} et al., Linear Algebra Appl. 564, 170--200 (2019; Zbl 1407.15010) Full Text: DOI arXiv Link
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
Bueno, M. I.; Dopico, F. M.; Furtado, S.; Medina, L. A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error. (English) Zbl 1416.65091 Calcolo 55, No. 3, Paper No. 32, 43 p. (2018). MSC: 65F15 65F35 15A54 PDFBibTeX XMLCite \textit{M. I. Bueno} et al., Calcolo 55, No. 3, Paper No. 32, 43 p. (2018; Zbl 1416.65091) Full Text: DOI Link
Dopico, Froilán M.; Lawrence, Piers W.; Pérez, Javier; Van Dooren, Paul Block Kronecker linearizations of matrix polynomials and their backward errors. (English) Zbl 1416.65094 Numer. Math. 140, No. 2, 373-426 (2018). MSC: 65F15 65F35 15A18 15A22 15A54 PDFBibTeX XMLCite \textit{F. M. Dopico} et al., Numer. Math. 140, No. 2, 373--426 (2018; Zbl 1416.65094) Full Text: DOI arXiv
Hook, James; Scott, Jennifer; Tisseur, Françoise; Hogg, Jonathan A Max-plus approach to incomplete Cholesky factorization preconditioners. (English) Zbl 1392.65031 SIAM J. Sci. Comput. 40, No. 4, A1987-A2004 (2018). MSC: 65F08 65F30 65F50 15A80 PDFBibTeX XMLCite \textit{J. Hook} et al., SIAM J. Sci. Comput. 40, No. 4, A1987--A2004 (2018; Zbl 1392.65031) Full Text: DOI
Akian, Marianne; Gaubert, Stéphane; Sharify, Meisam Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots. (English) Zbl 1428.15009 Linear Algebra Appl. 528, 394-435 (2017). Reviewer: Iveta Hnetynkova (Praha) MSC: 15A18 15A22 15A80 47J10 PDFBibTeX XMLCite \textit{M. Akian} et al., Linear Algebra Appl. 528, 394--435 (2017; Zbl 1428.15009) Full Text: DOI arXiv
Hook, James; Tisseur, Françoise Incomplete LU preconditioner based on max-plus approximation of LU factorization. (English) Zbl 1386.65102 SIAM J. Matrix Anal. Appl. 38, No. 4, 1160-1189 (2017). MSC: 65F08 65F30 15A23 15A80 PDFBibTeX XMLCite \textit{J. Hook} and \textit{F. Tisseur}, SIAM J. Matrix Anal. Appl. 38, No. 4, 1160--1189 (2017; Zbl 1386.65102) Full Text: DOI
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
Akian, Marianne; Bapat, Ravindra; Gaubert, Stéphane Non-archimedean valuations of eigenvalues of matrix polynomials. (English) Zbl 1341.15005 Linear Algebra Appl. 498, 592-627 (2016). MSC: 15A18 15A80 65F35 47A55 05C50 12K10 PDFBibTeX XMLCite \textit{M. Akian} et al., Linear Algebra Appl. 498, 592--627 (2016; Zbl 1341.15005) Full Text: DOI arXiv
De Terán, Fernando; Dopico, Froilán M.; van Dooren, Paul Matrix polynomials with completely prescribed eigenstructure. (English) Zbl 1315.15021 SIAM J. Matrix Anal. Appl. 36, No. 1, 302-328 (2015). MSC: 15A54 15A18 15A29 65F18 PDFBibTeX XMLCite \textit{F. De Terán} et al., SIAM J. Matrix Anal. Appl. 36, No. 1, 302--328 (2015; Zbl 1315.15021) Full Text: DOI Link
Lan, Hong; Meyer-Gohde, Alexander Solvability of perturbation solutions in DSGE models. (English) Zbl 1402.91374 J. Econ. Dyn. Control 45, 366-388 (2014). MSC: 91B62 91B51 15A24 65F30 PDFBibTeX XMLCite \textit{H. Lan} and \textit{A. Meyer-Gohde}, J. Econ. Dyn. Control 45, 366--388 (2014; Zbl 1402.91374) Full Text: DOI
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