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
Verde-Star, Luis Linearization and connection coefficients of polynomial sequences: a matrix approach. (English) Zbl 1518.15021 Linear Algebra Appl. 672, 195-209 (2023). Reviewer: Roberto S. Costas-Santos (Sevilla) MSC: 15A30 33C45 12D99 PDFBibTeX XMLCite \textit{L. Verde-Star}, Linear Algebra Appl. 672, 195--209 (2023; Zbl 1518.15021) Full Text: DOI arXiv
Pérez, Javier; Quintana, María C. Linearizations of rational matrices from general representations. (English) Zbl 1492.65092 Linear Algebra Appl. 647, 89-126 (2022). MSC: 65F15 15A18 15A22 15A54 93B18 93B60 PDFBibTeX XMLCite \textit{J. Pérez} and \textit{M. C. Quintana}, Linear Algebra Appl. 647, 89--126 (2022; Zbl 1492.65092) 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
Dopico, Froilán M.; Marcaida, Silvia; Quintana, María C.; Van Dooren, Paul Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems. (English) Zbl 1453.65076 Linear Algebra Appl. 604, 441-475 (2020). MSC: 65F15 15A18 15A22 93B18 PDFBibTeX XMLCite \textit{F. M. Dopico} et al., Linear Algebra Appl. 604, 441--475 (2020; Zbl 1453.65076) Full Text: DOI arXiv
Dopico, Froilán M.; Marcaida, Silvia; Quintana, María C. Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis. (English) Zbl 1416.65095 Linear Algebra Appl. 570, 1-45 (2019). MSC: 65F15 15A18 15A22 15A54 93B18 93B20 93B60 PDFBibTeX XMLCite \textit{F. M. Dopico} et al., Linear Algebra Appl. 570, 1--45 (2019; Zbl 1416.65095) Full Text: DOI arXiv Link
Das, Ranjan Kumar; Alam, Rafikul Affine spaces of strong linearizations for rational matrices and the recovery of eigenvectors and minimal bases. (English) Zbl 1416.65093 Linear Algebra Appl. 569, 335-368 (2019). MSC: 65F15 15B57 15A18 65F35 PDFBibTeX XMLCite \textit{R. K. Das} and \textit{R. Alam}, Linear Algebra Appl. 569, 335--368 (2019; Zbl 1416.65093) Full Text: DOI
Das, Ranjan Kumar; Alam, Rafikul Automatic recovery of eigenvectors and minimal bases of matrix polynomials from generalized Fiedler pencils with repetition. (English) Zbl 1416.65092 Linear Algebra Appl. 569, 78-112 (2019). MSC: 65F15 15B57 15A18 65F35 PDFBibTeX XMLCite \textit{R. K. Das} and \textit{R. Alam}, Linear Algebra Appl. 569, 78--112 (2019; Zbl 1416.65092) Full Text: DOI
Das, Ranjan Kumar; Alam, Rafikul Recovery of minimal bases and minimal indices of rational matrices from Fiedler-like pencils. (English) Zbl 1410.65113 Linear Algebra Appl. 566, 34-60 (2019). MSC: 65F15 15B57 15A18 65F35 PDFBibTeX XMLCite \textit{R. K. Das} and \textit{R. Alam}, Linear Algebra Appl. 566, 34--60 (2019; Zbl 1410.65113) Full Text: DOI
Chan, Eunice Y. S.; Corless, Robert M.; Gonzalez-Vega, Laureano; Sendra, J. Rafael; Sendra, Juana Algebraic linearizations of matrix polynomials. (English) Zbl 1433.15018 Linear Algebra Appl. 563, 373-399 (2019). Reviewer: Edgar Pereira (Natal) MSC: 15A22 15A21 65F60 PDFBibTeX XMLCite \textit{E. Y. S. Chan} et al., Linear Algebra Appl. 563, 373--399 (2019; Zbl 1433.15018) Full Text: DOI arXiv
Dopico, Froilán M.; Pérez, Javier; Van Dooren, Paul Block minimal bases \(\ell\)-ifications of matrix polynomials. (English) Zbl 1404.65020 Linear Algebra Appl. 562, 163-204 (2019). MSC: 65F15 15A18 15A21 15A22 15A54 93B18 PDFBibTeX XMLCite \textit{F. M. Dopico} et al., Linear Algebra Appl. 562, 163--204 (2019; Zbl 1404.65020) Full Text: DOI arXiv Link
Bliss, Nathan; Verschelde, Jan The method of Gauss-Newton to compute power series solutions of polynomial homotopies. (English) Zbl 1418.65068 Linear Algebra Appl. 542, 569-588 (2018). MSC: 65H10 PDFBibTeX XMLCite \textit{N. Bliss} and \textit{J. Verschelde}, Linear Algebra Appl. 542, 569--588 (2018; Zbl 1418.65068) 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
Faßbender, Heike; Saltenberger, Philip Block Kronecker ansatz spaces for matrix polynomials. (English) Zbl 1418.65047 Linear Algebra Appl. 542, 118-148 (2018). MSC: 65F15 15A03 15A18 15A22 15A23 47J10 PDFBibTeX XMLCite \textit{H. Faßbender} and \textit{P. Saltenberger}, Linear Algebra Appl. 542, 118--148 (2018; Zbl 1418.65047) Full Text: DOI arXiv
Perović, Vasilije; Mackey, D. Steven Linearizations of matrix polynomials in Newton bases. (English) Zbl 1398.65064 Linear Algebra Appl. 556, 1-45 (2018). MSC: 65F15 65D05 41A10 47J10 15A18 15A22 PDFBibTeX XMLCite \textit{V. Perović} and \textit{D. S. Mackey}, Linear Algebra Appl. 556, 1--45 (2018; Zbl 1398.65064) Full Text: DOI Link
Faßbender, Heike; Saltenberger, Philip On vector spaces of linearizations for matrix polynomials in orthogonal bases. (English) Zbl 1403.65017 Linear Algebra Appl. 525, 59-83 (2017). MSC: 65F15 15A18 15A22 15A54 PDFBibTeX XMLCite \textit{H. Faßbender} and \textit{P. Saltenberger}, Linear Algebra Appl. 525, 59--83 (2017; Zbl 1403.65017) Full Text: DOI arXiv
Bueno, M. I.; Breen, J.; Ford, S.; Furtado, S. On the sign characteristic of Hermitian linearizations in \(\mathbb{DL}(P)\). (English) Zbl 1358.65023 Linear Algebra Appl. 519, 73-101 (2017). MSC: 65F15 15A22 15B57 PDFBibTeX XMLCite \textit{M. I. Bueno} et al., Linear Algebra Appl. 519, 73--101 (2017; Zbl 1358.65023) Full Text: DOI
Alam, Rafikul; Behera, Namita Recovery of eigenvectors of rational matrix functions from Fiedler-like linearizations. (English) Zbl 1352.65115 Linear Algebra Appl. 510, 373-394 (2016). MSC: 65F15 15B57 15A18 65F35 PDFBibTeX XMLCite \textit{R. Alam} and \textit{N. Behera}, Linear Algebra Appl. 510, 373--394 (2016; Zbl 1352.65115) Full Text: DOI
Mackey, D. Steven; Perović, Vasilije Linearizations of matrix polynomials in Bernstein bases. (English) Zbl 1334.65044 Linear Algebra Appl. 501, 162-197 (2016). MSC: 65D17 65F15 15A18 15A21 15A22 41A10 PDFBibTeX XMLCite \textit{D. S. Mackey} and \textit{V. Perović}, Linear Algebra Appl. 501, 162--197 (2016; Zbl 1334.65044) Full Text: DOI
De Terán, Fernando; Dopico, Froilán M.; Van Dooren, Paul Constructing strong \(\ell\)-ifications from dual minimal bases. (English) Zbl 1333.65044 Linear Algebra Appl. 495, 344-372 (2016). MSC: 65F30 15A54 15A18 PDFBibTeX XMLCite \textit{F. De Terán} et al., Linear Algebra Appl. 495, 344--372 (2016; Zbl 1333.65044) Full Text: DOI
Liesen, Jörg; Luce, Robert Fast recovery and approximation of hidden Cauchy structure. (English) Zbl 1329.15060 Linear Algebra Appl. 493, 261-280 (2016). MSC: 15B05 65Y20 65F20 PDFBibTeX XMLCite \textit{J. Liesen} and \textit{R. Luce}, Linear Algebra Appl. 493, 261--280 (2016; Zbl 1329.15060) Full Text: DOI arXiv
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
Mackey, D. Steven; Mackey, Niloufer; Mehl, Christian; Mehrmann, Volker Möbius transformations of matrix polynomials. (English) Zbl 1309.65042 Linear Algebra Appl. 470, 120-184 (2015). MSC: 65F15 15A18 15A21 15A54 15B57 PDFBibTeX XMLCite \textit{D. S. Mackey} et al., Linear Algebra Appl. 470, 120--184 (2015; Zbl 1309.65042) Full Text: DOI
Karow, Michael; Mengi, Emre Matrix polynomials with specified eigenvalues. (English) Zbl 1303.65019 Linear Algebra Appl. 466, 457-482 (2015). MSC: 65F18 15A54 15A18 PDFBibTeX XMLCite \textit{M. Karow} and \textit{E. Mengi}, Linear Algebra Appl. 466, 457--482 (2015; Zbl 1303.65019) Full Text: DOI arXiv
Bueno, M. I.; Furtado, S. Structured strong linearizations from Fiedler pencils with repetition. II. (English) Zbl 1310.65042 Linear Algebra Appl. 463, 282-321 (2014). MSC: 65F15 15A18 15A22 PDFBibTeX XMLCite \textit{M. I. Bueno} and \textit{S. Furtado}, Linear Algebra Appl. 463, 282--321 (2014; Zbl 1310.65042) Full Text: DOI
Bueno, M. I.; Curlett, K.; Furtado, S. Structured strong linearizations from Fiedler pencils with repetition. I. (English) Zbl 1298.65064 Linear Algebra Appl. 460, 51-80 (2014). MSC: 65F15 15A18 15A22 93B18 PDFBibTeX XMLCite \textit{M. I. Bueno} et al., Linear Algebra Appl. 460, 51--80 (2014; Zbl 1298.65064) Full Text: DOI
De Terán, Fernando; Dopico, Froilán M.; Mackey, D. Steven Spectral equivalence of matrix polynomials and the index sum theorem. (English) Zbl 1297.65038 Linear Algebra Appl. 459, 264-333 (2014). MSC: 65F15 15A18 15A21 15A22 15A54 PDFBibTeX XMLCite \textit{F. De Terán} et al., Linear Algebra Appl. 459, 264--333 (2014; Zbl 1297.65038) Full Text: DOI
Johansson, Stefan; Kågström, Bo; Van Dooren, Paul Stratification of full rank polynomial matrices. (English) Zbl 1281.15019 Linear Algebra Appl. 439, No. 4, 1062-1090 (2013). MSC: 15A54 15A22 15A18 PDFBibTeX XMLCite \textit{S. Johansson} et al., Linear Algebra Appl. 439, No. 4, 1062--1090 (2013; Zbl 1281.15019) Full Text: DOI
Mackey, D. Steven The continuing influence of Fiedler’s work on companion matrices. (English) Zbl 1281.15008 Linear Algebra Appl. 439, No. 4, 810-817 (2013). MSC: 15A18 15A22 15A23 15A54 15B99 15-03 PDFBibTeX XMLCite \textit{D. S. Mackey}, Linear Algebra Appl. 439, No. 4, 810--817 (2013; Zbl 1281.15008) Full Text: DOI
Mackey, D. Steven; Mackey, Niloufer; Mehl, Christian; Mehrmann, Volker Skew-symmetric matrix polynomials and their Smith forms. (English) Zbl 1281.15020 Linear Algebra Appl. 438, No. 12, 4625-4653 (2013). MSC: 15A54 15A16 15A21 15A23 15A24 PDFBibTeX XMLCite \textit{D. S. Mackey} et al., Linear Algebra Appl. 438, No. 12, 4625--4653 (2013; Zbl 1281.15020) Full Text: DOI
Tian, Yongge Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications. (English) Zbl 1252.15026 Linear Algebra Appl. 437, No. 3, 835-859 (2012). Reviewer: Süleyman Güler (Aydin) MSC: 15A54 15A24 15A63 15B57 90C20 90C22 15B48 15A18 65K05 15A45 15A03 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Algebra Appl. 437, No. 3, 835--859 (2012; Zbl 1252.15026) Full Text: DOI
Hochstenbach, Michiel E.; Muhič, Andrej; Plestenjak, Bor On linearizations of the quadratic two-parameter eigenvalue problem. (English) Zbl 1245.65042 Linear Algebra Appl. 436, No. 8, 2725-2743 (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65F15 PDFBibTeX XMLCite \textit{M. E. Hochstenbach} et al., Linear Algebra Appl. 436, No. 8, 2725--2743 (2012; Zbl 1245.65042) Full Text: DOI
Adhikari, Bibhas; Alam, Rafikul; Kressner, Daniel Structured eigenvalue condition numbers and linearizations for matrix polynomials. (English) Zbl 1225.65043 Linear Algebra Appl. 435, No. 9, 2193-2221 (2011). Reviewer: R. Militaru (Craiova) MSC: 65F15 65F35 15B57 15A54 PDFBibTeX XMLCite \textit{B. Adhikari} et al., Linear Algebra Appl. 435, No. 9, 2193--2221 (2011; Zbl 1225.65043) Full Text: DOI
Czornik, Adam; Nawrat, Aleksander Stability by the linear approximation for discrete equations. (English) Zbl 1214.93087 Linear Algebra Appl. 435, No. 4, 742-750 (2011). MSC: 93D20 93C55 93C05 93B18 PDFBibTeX XMLCite \textit{A. Czornik} and \textit{A. Nawrat}, Linear Algebra Appl. 435, No. 4, 742--750 (2011; Zbl 1214.93087) 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
Adhikari, Bibhas; Alam, Rafikul On backward errors of structured polynomial eigenproblems solved by structure preserving linearizations. (English) Zbl 1215.65065 Linear Algebra Appl. 434, No. 9, 1989-2017 (2011). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F15 15A18 65F35 PDFBibTeX XMLCite \textit{B. Adhikari} and \textit{R. Alam}, Linear Algebra Appl. 434, No. 9, 1989--2017 (2011; Zbl 1215.65065) Full Text: DOI arXiv
Mackey, D. Steven; Mackey, Niloufer; Mehl, Christian; Mehrmann, Volker Jordan structures of alternating matrix polynomials. (English) Zbl 1188.15010 Linear Algebra Appl. 432, No. 4, 867-891 (2010). Reviewer: R. Militaru (Craiova) MSC: 15A21 15A18 15A54 PDFBibTeX XMLCite \textit{D. S. Mackey} et al., Linear Algebra Appl. 432, No. 4, 867--891 (2010; Zbl 1188.15010) Full Text: DOI
Leventides, John; Karcanias, Nicos Zero assignment of matrix pencils by additive structured transformations. (English) Zbl 1173.15004 Linear Algebra Appl. 431, No. 8, 1380-1396 (2009). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15A22 94C05 PDFBibTeX XMLCite \textit{J. Leventides} and \textit{N. Karcanias}, Linear Algebra Appl. 431, No. 8, 1380--1396 (2009; Zbl 1173.15004) Full Text: DOI Link
Byers, Ralph; Mehrmann, Volker; Xu, Hongguo Trimmed linearizations for structured matrix polynomials. (English) Zbl 1155.65026 Linear Algebra Appl. 429, No. 10, 2373-2400 (2008). Reviewer: Petko Hr. Petkov (Sofia) MSC: 65F15 15A21 15A54 PDFBibTeX XMLCite \textit{R. Byers} et al., Linear Algebra Appl. 429, No. 10, 2373--2400 (2008; Zbl 1155.65026) Full Text: DOI
Psarrakos, Panayiotis J.; Tsatsomeros, Michael J. A primer of Perron–Frobenius theory for matrix polynomials. (English) Zbl 1063.15019 Linear Algebra Appl. 393, 333-351 (2004). Reviewer: Grosio Stanilov (Sofia) MSC: 15B48 15A18 15A54 PDFBibTeX XMLCite \textit{P. J. Psarrakos} and \textit{M. J. Tsatsomeros}, Linear Algebra Appl. 393, 333--351 (2004; Zbl 1063.15019) Full Text: DOI
Kalogeropoulos, G.; Psarrakos, P.; Karcanias, N. On the computation of the Jordan canonical form of regular matrix polynomials. (English) Zbl 1057.65019 Linear Algebra Appl. 385, 117-130 (2004). Reviewer: Raffaella Pavani (Milano) MSC: 65F30 15A21 15A22 PDFBibTeX XMLCite \textit{G. Kalogeropoulos} et al., Linear Algebra Appl. 385, 117--130 (2004; Zbl 1057.65019) Full Text: DOI
Förster, K.-H.; Nagy, B. On spectra of expansion graphs and matrix polynomials. (English) Zbl 1016.05051 Linear Algebra Appl. 363, 89-101 (2003). Reviewer: Ian M.Wanless (Oxford) MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{K. H. Förster} and \textit{B. Nagy}, Linear Algebra Appl. 363, 89--101 (2003; Zbl 1016.05051) Full Text: DOI
Ćurgus, Branko; Dijksma, Aad; Read, Tom The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces. (English) Zbl 0996.47025 Linear Algebra Appl. 329, No. 1-3, 97-136 (2001). Reviewer: Th.M.Rassias (Athens) MSC: 47A75 46E22 47A06 PDFBibTeX XMLCite \textit{B. Ćurgus} et al., Linear Algebra Appl. 329, No. 1--3, 97--136 (2001; Zbl 0996.47025) Full Text: DOI