Miyajima, Shinya Fast verified computation for real powers of large matrices with Kronecker structure. (English) Zbl 07702357 Appl. Math. Comput. 453, Article ID 128055, 22 p. (2023). MSC: 15A16 65F60 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Appl. Math. Comput. 453, Article ID 128055, 22 p. (2023; Zbl 07702357) Full Text: DOI
Rump, Siegfried M. Verified error bounds for all eigenvalues and eigenvectors of a matrix. (English) Zbl 1508.65034 SIAM J. Matrix Anal. Appl. 43, No. 4, 1736-1754 (2022). MSC: 65F15 15A42 65G30 PDFBibTeX XMLCite \textit{S. M. Rump}, SIAM J. Matrix Anal. Appl. 43, No. 4, 1736--1754 (2022; Zbl 1508.65034) Full Text: DOI
Rump, S. M. Entrywise lower and upper bounds for the Perron vector. (English) Zbl 1501.15015 Linear Algebra Appl. 653, 314-319 (2022). MSC: 15A45 15B48 15A42 PDFBibTeX XMLCite \textit{S. M. Rump}, Linear Algebra Appl. 653, 314--319 (2022; Zbl 1501.15015) Full Text: DOI
Miyajima, Shinya Fast enclosure for the minimal nonnegative solution to the nonsymmetric T-Riccati equation. (English) Zbl 1498.65058 Calcolo 59, No. 3, Paper No. 31, 16 p. (2022). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{S. Miyajima}, Calcolo 59, No. 3, Paper No. 31, 16 p. (2022; Zbl 1498.65058) Full Text: DOI
Miyajima, Shinya Verified computation of matrix gamma function. (English) Zbl 1497.65082 Linear Multilinear Algebra 70, No. 7, 1207-1229 (2022). MSC: 65F60 65G20 15A16 PDFBibTeX XMLCite \textit{S. Miyajima}, Linear Multilinear Algebra 70, No. 7, 1207--1229 (2022; Zbl 1497.65082) Full Text: DOI arXiv
Miyajima, Shinya Fast verified computation for positive solutions to \(\mathcal{M} \)-tensor multi-linear systems and Perron vectors of a kind of weakly irreducible nonnegative tensors. (English) Zbl 1490.65085 J. Comput. Appl. Math. 406, Article ID 113930, 15 p. (2022). MSC: 65F99 15A69 65F10 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, J. Comput. Appl. Math. 406, Article ID 113930, 15 p. (2022; Zbl 1490.65085) Full Text: DOI
Li, Zhe; Zhang, Chunlei The verification of multiplicity support of a defective eigenvalue of a real matrix. (English) Zbl 1510.65067 Appl. Math. Comput. 414, Article ID 126671, 15 p. (2022). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{Z. Li} and \textit{C. Zhang}, Appl. Math. Comput. 414, Article ID 126671, 15 p. (2022; Zbl 1510.65067) Full Text: DOI
Hartman, David; Hladík, Milan; Říha, David Computing the spectral decomposition of interval matrices and a study on interval matrix powers. (English) Zbl 1510.65094 Appl. Math. Comput. 403, Article ID 126174, 13 p. (2021). MSC: 65G40 15A18 PDFBibTeX XMLCite \textit{D. Hartman} et al., Appl. Math. Comput. 403, Article ID 126174, 13 p. (2021; Zbl 1510.65094) Full Text: DOI arXiv
Miyajima, Shinya Fast verification for the Perron pair of an irreducible nonnegative matrix. (English) Zbl 07373353 Electron. J. Linear Algebra 37, 402-415 (2021). MSC: 65F15 15A18 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Electron. J. Linear Algebra 37, 402--415 (2021; Zbl 07373353) Full Text: Link
Miyajima, Shinya Computing enclosures for the matrix Mittag-Leffler function. (English) Zbl 1470.65080 J. Sci. Comput. 87, No. 2, Paper No. 62, 22 p. (2021). MSC: 65F60 15A16 65G20 26A33 33E12 33F05 PDFBibTeX XMLCite \textit{S. Miyajima}, J. Sci. Comput. 87, No. 2, Paper No. 62, 22 p. (2021; Zbl 1470.65080) Full Text: DOI
Lange, Marko; Rump, Siegfried M. Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin’s \(\sin (\theta)\) theorem. (English) Zbl 1470.65088 BIT 61, No. 1, 361-380 (2021). MSC: 65F99 15A03 PDFBibTeX XMLCite \textit{M. Lange} and \textit{S. M. Rump}, BIT 61, No. 1, 361--380 (2021; Zbl 1470.65088) Full Text: DOI
Miyajima, Shinya Verified computation of real powers of matrices. (English) Zbl 1461.65065 J. Comput. Appl. Math. 391, Article ID 113431, 13 p. (2021). MSC: 65F60 15A16 PDFBibTeX XMLCite \textit{S. Miyajima}, J. Comput. Appl. Math. 391, Article ID 113431, 13 p. (2021; Zbl 1461.65065) Full Text: DOI
Frommer, Andreas; Hashemi, Behnam Computing enclosures for the matrix exponential. (English) Zbl 1459.65056 SIAM J. Matrix Anal. Appl. 41, No. 4, 1674-1703 (2020). MSC: 65F60 65G20 15A16 PDFBibTeX XMLCite \textit{A. Frommer} and \textit{B. Hashemi}, SIAM J. Matrix Anal. Appl. 41, No. 4, 1674--1703 (2020; Zbl 1459.65056) Full Text: DOI
Li, Zhe; Wang, Xueqing Verified error bounds for real eigenvalues of real symmetric and persymmetric matrices. (English) Zbl 1459.65047 Math. Probl. Eng. 2020, Article ID 9240852, 9 p. (2020). MSC: 65F15 15A18 65F35 PDFBibTeX XMLCite \textit{Z. Li} and \textit{X. Wang}, Math. Probl. Eng. 2020, Article ID 9240852, 9 p. (2020; Zbl 1459.65047) Full Text: DOI
Bozorgmanesh, Hassan; Hajarian, Masoud; Chronopoulos, Anthony Theodore Interval tensors and their application in solving multi-linear systems of equations. (English) Zbl 1448.15030 Comput. Math. Appl. 79, No. 3, 697-715 (2020). MSC: 15A69 15A18 15A06 65F10 PDFBibTeX XMLCite \textit{H. Bozorgmanesh} et al., Comput. Math. Appl. 79, No. 3, 697--715 (2020; Zbl 1448.15030) Full Text: DOI
Miyajima, Shinya Enclosing Moore-Penrose inverses. (English) Zbl 1436.15005 Calcolo 57, No. 1, Paper No. 7, 16 p. (2020). MSC: 15A09 65F20 PDFBibTeX XMLCite \textit{S. Miyajima}, Calcolo 57, No. 1, Paper No. 7, 16 p. (2020; Zbl 1436.15005) Full Text: DOI
Rump, Siegfried M. Verified bounds for the determinant of real or complex point or interval matrices. (English) Zbl 1437.65020 J. Comput. Appl. Math. 372, Article ID 112610, 10 p. (2020). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F40 65F22 65F08 15A15 15A23 65G20 PDFBibTeX XMLCite \textit{S. M. Rump}, J. Comput. Appl. Math. 372, Article ID 112610, 10 p. (2020; Zbl 1437.65020) Full Text: DOI
Liu, Xuefeng Explicit eigenvalue bounds of differential operators defined by symmetric positive semi-definite bilinear forms. (English) Zbl 1433.65054 J. Comput. Appl. Math. 371, Article ID 112666, 7 p. (2020). MSC: 65F15 15A18 15A63 PDFBibTeX XMLCite \textit{X. Liu}, J. Comput. Appl. Math. 371, Article ID 112666, 7 p. (2020; Zbl 1433.65054) Full Text: DOI arXiv
Stanimirović, Predrag S.; Roy, Falguni; Gupta, Dharmendra K.; Srivastava, Shwetabh Computing the Moore-Penrose inverse using its error bounds. (English) Zbl 1435.65061 Appl. Math. Comput. 371, Article ID 124957, 13 p. (2020). MSC: 65F20 15A09 65F10 PDFBibTeX XMLCite \textit{P. S. Stanimirović} et al., Appl. Math. Comput. 371, Article ID 124957, 13 p. (2020; Zbl 1435.65061) Full Text: DOI
Miyajima, Shinya Verified computation for the matrix Lambert \(W\) function. (English) Zbl 1433.65088 Appl. Math. Comput. 362, Article ID 124555, 15 p. (2019). MSC: 65G30 15A15 15A16 65F60 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Appl. Math. Comput. 362, Article ID 124555, 15 p. (2019; Zbl 1433.65088) Full Text: DOI
Miyajima, Shinya Robust verification algorithm for stabilizing solutions of discrete-time algebraic Riccati equations. (English) Zbl 1437.65025 Japan J. Ind. Appl. Math. 36, No. 3, 763-776 (2019). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{S. Miyajima}, Japan J. Ind. Appl. Math. 36, No. 3, 763--776 (2019; Zbl 1437.65025) Full Text: DOI
Miyajima, Shinya Verified computation for the matrix principal logarithm. (English) Zbl 1434.65057 Linear Algebra Appl. 569, 38-61 (2019). MSC: 65F60 15A16 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Linear Algebra Appl. 569, 38--61 (2019; Zbl 1434.65057) Full Text: DOI
Miyajima, Shinya Verified computation of the matrix exponential. (English) Zbl 1447.65009 Adv. Comput. Math. 45, No. 1, 137-152 (2019). Reviewer: John D. Dixon (Ottawa) MSC: 65F60 15A16 PDFBibTeX XMLCite \textit{S. Miyajima}, Adv. Comput. Math. 45, No. 1, 137--152 (2019; Zbl 1447.65009) Full Text: DOI
Miyajima, Shinya Verified computation for the Hermitian positive definite solution of the conjugate discrete-time algebraic Riccati equation. (English) Zbl 1417.65123 J. Comput. Appl. Math. 350, 80-86 (2019). MSC: 65F30 15A24 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, J. Comput. Appl. Math. 350, 80--86 (2019; Zbl 1417.65123) Full Text: DOI
Haqiri, Tayyebe; Mohseni Moghadam, Mahmoud; Rivaz, Azim The united stable solution set of interval continuous-time algebraic Riccati equation and verified numerical computation of its outer estimation. (English) Zbl 1424.65051 Turk. J. Math. 42, No. 3, 1130-1155 (2018). MSC: 65F30 15A24 65G30 PDFBibTeX XMLCite \textit{T. Haqiri} et al., Turk. J. Math. 42, No. 3, 1130--1155 (2018; Zbl 1424.65051) Full Text: DOI
Miyajima, Shinya Fast verified computation for the solution of the T-congruence Sylvester equation. (English) Zbl 1434.65047 Japan J. Ind. Appl. Math. 35, No. 2, 541-551 (2018). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F45 15A24 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Japan J. Ind. Appl. Math. 35, No. 2, 541--551 (2018; Zbl 1434.65047) Full Text: DOI
Miyajima, Shinya Fast verified computation for the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation. (English) Zbl 1432.65051 Comput. Appl. Math. 37, No. 4, 4599-4610 (2018). MSC: 65F45 15A24 65G20 65H10 PDFBibTeX XMLCite \textit{S. Miyajima}, Comput. Appl. Math. 37, No. 4, 4599--4610 (2018; Zbl 1432.65051) Full Text: DOI
Ghanbari, Mojtaba An estimation of algebraic solution for a complex interval linear system. (English) Zbl 1398.65045 Soft Comput. 22, No. 9, 2881-2890 (2018). MSC: 65F10 65G30 15A06 15B15 PDFBibTeX XMLCite \textit{M. Ghanbari}, Soft Comput. 22, No. 9, 2881--2890 (2018; Zbl 1398.65045) Full Text: DOI
Roy, Falguni; Gupta, D. K.; Stanimirović, Predrag S. An interval extension of SMS method for computing weighted Moore-Penrose inverse. (English) Zbl 1397.65060 Calcolo 55, No. 2, Paper No. 15, 21 p. (2018). Reviewer: Constantin Popa (Constanţa) MSC: 65F20 15A09 65G30 PDFBibTeX XMLCite \textit{F. Roy} et al., Calcolo 55, No. 2, Paper No. 15, 21 p. (2018; Zbl 1397.65060) Full Text: DOI
Miyajima, Shinya Fast verified computation for the solvent of the quadratic matrix equation. (English) Zbl 1391.65108 Electron. J. Linear Algebra 34, 137-151 (2018). MSC: 65F30 15A24 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Electron. J. Linear Algebra 34, 137--151 (2018; Zbl 1391.65108)
Miyajima, Shinya Fast verified computation for solutions of algebraic Riccati equations arising in transport theory. (English) Zbl 1438.65080 Numer. Linear Algebra Appl. 24, No. 5, e2098, 12 p. (2017). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{S. Miyajima}, Numer. Linear Algebra Appl. 24, No. 5, e2098, 12 p. (2017; Zbl 1438.65080) Full Text: DOI
Miyajima, Shinya Fast verified computation for stabilizing solutions of discrete-time algebraic Riccati equations. (English) Zbl 1360.65127 J. Comput. Appl. Math. 319, 352-364 (2017). MSC: 65F30 15A24 93C55 93C05 65G30 65F10 PDFBibTeX XMLCite \textit{S. Miyajima}, J. Comput. Appl. Math. 319, 352--364 (2017; Zbl 1360.65127) Full Text: DOI
Chen, Yunkun; Shi, Xinghua; Wei, Yimin Convergence of Rump’s method for computing the Moore-Penrose inverse. (English) Zbl 1413.65115 Czech. Math. J. 66, No. 3, 859-879 (2016). Reviewer: Liu Xinguo (Qingdao) MSC: 65F20 15A09 65F35 15A24 PDFBibTeX XMLCite \textit{Y. Chen} et al., Czech. Math. J. 66, No. 3, 859--879 (2016; Zbl 1413.65115) Full Text: DOI Link
Sharaya, Irene A. Boundary intervals method for visualization of polyhedral solution sets. (Russian. English summary) Zbl 1417.65128 Vychisl. Tekhnol. 20, No. 1, 75-103 (2015). MSC: 65G40 52B10 15A39 PDFBibTeX XMLCite \textit{I. A. Sharaya}, Vychisl. Tekhnol. 20, No. 1, 75--103 (2015; Zbl 1417.65128) Full Text: Link
Miyajima, Shinya Fast enclosure for the minimum norm least squares solution of the matrix equation \(AXB=C\). (English) Zbl 1363.65079 Numer. Linear Algebra Appl. 22, No. 3, 548-563 (2015). MSC: 65F30 65F20 15A24 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Numer. Linear Algebra Appl. 22, No. 3, 548--563 (2015; Zbl 1363.65079) Full Text: DOI
Toyonaga, Kenji; Johnson, Charles R. Application of an identity for subtrees with a given eigenvalue. (English) Zbl 1330.05042 Electron. J. Linear Algebra 30, 964-973 (2015). MSC: 05C05 05C50 15A18 13H15 PDFBibTeX XMLCite \textit{K. Toyonaga} and \textit{C. R. Johnson}, Electron. J. Linear Algebra 30, 964--973 (2015; Zbl 1330.05042) Full Text: DOI
Miyajima, Shinya Fast verified computation for solutions of continuous-time algebraic Riccati equations. (English) Zbl 1329.65093 Japan J. Ind. Appl. Math. 32, No. 2, 529-544 (2015). Reviewer: Michael Jung (Dresden) MSC: 65G20 15A24 65F30 93C05 65G30 PDFBibTeX XMLCite \textit{S. Miyajima}, Japan J. Ind. Appl. Math. 32, No. 2, 529--544 (2015; Zbl 1329.65093) Full Text: DOI
Dehghani-Madiseh, Marzieh; Dehghan, Mehdi Generalized solution sets of the interval generalized Sylvester matrix equation \(\sum_{i=1}^p\mathbf A_iX_i+\sum_{j=1}^qY_j\mathbf B_j=\mathbf C\) and some approaches for inner and outer estimations. (English) Zbl 1368.15012 Comput. Math. Appl. 68, No. 12, Part A, 1758-1774 (2014). MSC: 15A24 65F30 65G40 PDFBibTeX XMLCite \textit{M. Dehghani-Madiseh} and \textit{M. Dehghan}, Comput. Math. Appl. 68, No. 12, Part A, 1758--1774 (2014; Zbl 1368.15012) Full Text: DOI
Behera, Diptiranjan; Chakraverty, S. Solving fuzzy complex system of linear equations. (English) Zbl 1354.15021 Inf. Sci. 277, 154-162 (2014); erratum ibid. 369, 788-790 (2016). MSC: 15B15 15A06 PDFBibTeX XMLCite \textit{D. Behera} and \textit{S. Chakraverty}, Inf. Sci. 277, 154--162 (2014; Zbl 1354.15021) Full Text: DOI
Kolev, Lubomir V. Parameterized solution of linear interval parametric systems. (English) Zbl 1338.65069 Appl. Math. Comput. 246, 229-246 (2014). MSC: 65F05 65G40 15A06 PDFBibTeX XMLCite \textit{L. V. Kolev}, Appl. Math. Comput. 246, 229--246 (2014; Zbl 1338.65069) Full Text: DOI
Miyajima, Shinya Fast enclosure for all eigenvalues and invariant subspaces in generalized eigenvalue problems. (English) Zbl 1307.65044 SIAM J. Matrix Anal. Appl. 35, No. 3, 1205-1225 (2014). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 65F15 15A42 PDFBibTeX XMLCite \textit{S. Miyajima}, SIAM J. Matrix Anal. Appl. 35, No. 3, 1205--1225 (2014; Zbl 1307.65044) Full Text: DOI
Frommer, Andreas; Hashemi, Behnam; Sablik, Thomas Computing enclosures for the inverse square root and the sign function of a matrix. (English) Zbl 1293.65071 Linear Algebra Appl. 456, 199-213 (2014). MSC: 65F30 15A24 65G30 65G20 PDFBibTeX XMLCite \textit{A. Frommer} et al., Linear Algebra Appl. 456, 199--213 (2014; Zbl 1293.65071) Full Text: DOI
Miyajima, Shinya Componentwise enclosure for solutions of least squares problems and underdetermined systems. (English) Zbl 1329.65081 Linear Algebra Appl. 444, 28-41 (2014). MSC: 65F20 15A06 65G50 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Linear Algebra Appl. 444, 28--41 (2014; Zbl 1329.65081) Full Text: DOI
Castelli, Roberto; Lessard, Jean-Philippe A method to rigorously enclose eigenpairs of complex interval matrices. (English) Zbl 1340.65057 Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 21-31 (2013). MSC: 65F15 65G30 15A42 PDFBibTeX XMLCite \textit{R. Castelli} and \textit{J.-P. Lessard}, in: Proceedings of the international conference `Applications of mathematics', Prague, Czech Republic, May 15--17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 21--31 (2013; Zbl 1340.65057) Full Text: arXiv Link
Hashemi, Behnam; Dehghan, Mehdi The interval Lyapunov matrix equation: analytical results and an efficient numerical technique for outer estimation of the united solution set. (English) Zbl 1255.15002 Math. Comput. Modelling 55, No. 3-4, 622-633 (2012). MSC: 15A06 65F30 65G40 PDFBibTeX XMLCite \textit{B. Hashemi} and \textit{M. Dehghan}, Math. Comput. Modelling 55, No. 3--4, 622--633 (2012; Zbl 1255.15002) Full Text: DOI
Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shin’ichi; Rump, Siegfried M. Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications. (English) Zbl 1244.65062 Numer. Algorithms 59, No. 1, 95-118 (2012). Reviewer: Frank Uhlig (Auburn) MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{K. Ozaki} et al., Numer. Algorithms 59, No. 1, 95--118 (2012; Zbl 1244.65062) Full Text: DOI
Frommer, Andreas; Hashemi, Behnam Verified error bounds for solutions of Sylvester matrix equations. (English) Zbl 1236.65045 Linear Algebra Appl. 436, No. 2, 405-420 (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65F30 15A24 65F05 65G20 65G30 PDFBibTeX XMLCite \textit{A. Frommer} and \textit{B. Hashemi}, Linear Algebra Appl. 436, No. 2, 405--420 (2012; Zbl 1236.65045) Full Text: DOI
Wang, Aixiang; Wang, Haijun; Deng, Yongkun Interval algorithm for absolute value equations. (English) Zbl 1236.65047 Cent. Eur. J. Math. 9, No. 5, 1171-1184 (2011). Reviewer: M. Milla Miranda (Rio de Janeiro) MSC: 65G30 15A06 PDFBibTeX XMLCite \textit{A. Wang} et al., Cent. Eur. J. Math. 9, No. 5, 1171--1184 (2011; Zbl 1236.65047) Full Text: DOI
Rump, Siegfried M. Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse. (English) Zbl 1226.65028 BIT 51, No. 2, 367-384 (2011). Reviewer: Constantin Popa (Constanţa) MSC: 65F15 65F20 65G20 15A18 15A60 PDFBibTeX XMLCite \textit{S. M. Rump}, BIT 51, No. 2, 367--384 (2011; Zbl 1226.65028) Full Text: DOI
Hashemi, Behnam; Dehghan, Mehdi Results concerning interval linear systems with multiple right-hand sides and the interval matrix equation \(AX=B\). (English) Zbl 1221.65087 J. Comput. Appl. Math. 235, No. 9, 2969-2978 (2011). Reviewer: Günter Mayer (Rostock) MSC: 65F05 65G30 15A24 PDFBibTeX XMLCite \textit{B. Hashemi} and \textit{M. Dehghan}, J. Comput. Appl. Math. 235, No. 9, 2969--2978 (2011; Zbl 1221.65087) Full Text: DOI
Ogita, Takeshi Accurate matrix factorization: Inverse LU and inverse QR factorizations. (English) Zbl 1215.65051 SIAM J. Matrix Anal. Appl. 31, No. 5, 2477-2497 (2010). Reviewer: Edgar Pereira (Covilha) MSC: 65F05 65G20 15A23 65F22 PDFBibTeX XMLCite \textit{T. Ogita}, SIAM J. Matrix Anal. Appl. 31, No. 5, 2477--2497 (2010; Zbl 1215.65051) Full Text: DOI
Kolev, Lubomir Eigenvalue range determination for interval and parametric matrices. (English) Zbl 1298.94156 Int. J. Circuit Theory Appl. 38, No. 10, 1027-1061 (2010). MSC: 94C05 65F10 65F15 15A60 PDFBibTeX XMLCite \textit{L. Kolev}, Int. J. Circuit Theory Appl. 38, No. 10, 1027--1061 (2010; Zbl 1298.94156) Full Text: DOI
Frommer, Andreas; Hashemi, Behnam Verified computation of square roots of a matrix. (English) Zbl 1194.65069 SIAM J. Matrix Anal. Appl. 31(2009), No. 3, 1279-1302 (2010). MSC: 65F60 15A24 65G20 65G30 PDFBibTeX XMLCite \textit{A. Frommer} and \textit{B. Hashemi}, SIAM J. Matrix Anal. Appl. 31, No. 3, 1279--1302 (2010; Zbl 1194.65069) Full Text: DOI
Leng, Huinan; He, Zhiqing Computation of bounds for eigenvalues of structures with interval parameters. (English) Zbl 1193.65036 Appl. Math. Comput. 216, No. 9, 2734-2739 (2010). MSC: 65F15 15A42 65G30 PDFBibTeX XMLCite \textit{H. Leng} and \textit{Z. He}, Appl. Math. Comput. 216, No. 9, 2734--2739 (2010; Zbl 1193.65036) Full Text: DOI
Miyajima, Shinya Fast enclosure for all eigenvalues in generalized eigenvalue problems. (English) Zbl 1188.65043 J. Comput. Appl. Math. 233, No. 11, 2994-3004 (2010). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65F15 65G20 65G50 15A42 PDFBibTeX XMLCite \textit{S. Miyajima}, J. Comput. Appl. Math. 233, No. 11, 2994--3004 (2010; Zbl 1188.65043) Full Text: DOI
Rump, Siegfried M. Inversion of extremely ill-conditioned matrices in floating-point. (English) Zbl 1185.65050 Japan J. Ind. Appl. Math. 26, No. 2-3, 249-277 (2009). MSC: 65F05 65G50 65F35 15A12 PDFBibTeX XMLCite \textit{S. M. Rump}, Japan J. Ind. Appl. Math. 26, No. 2--3, 249--277 (2009; Zbl 1185.65050) Full Text: DOI Euclid
Toyonaga, Kenji Numerical enclosure for multiple eigenvalues of an Hermitian matrix whose graph is a tree. (English) Zbl 1183.65038 Linear Algebra Appl. 431, No. 11, 1989-1999 (2009). Reviewer: Thomas Sonar (Braunschweig) MSC: 65F15 05C50 15A42 15B57 PDFBibTeX XMLCite \textit{K. Toyonaga}, Linear Algebra Appl. 431, No. 11, 1989--1999 (2009; Zbl 1183.65038) Full Text: DOI
Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin’ichi Accurate floating-point summation. I: Faithful rounding. (English) Zbl 1185.65082 SIAM J. Sci. Comput. 31, No. 1, 189-224 (2008). MSC: 65G50 65F35 15-04 65G99 65-04 PDFBibTeX XMLCite \textit{S. M. Rump} et al., SIAM J. Sci. Comput. 31, No. 1, 189--224 (2008; Zbl 1185.65082) Full Text: DOI
Toyonaga, K. A method for separating nearly multiple eigenvalues for Hermitian matrix. (English) Zbl 1112.65032 J. Comput. Appl. Math. 199, No. 2, 432-436 (2007). Reviewer: Ludwig Elsner (Bielefeld) MSC: 65F15 65G20 15A42 PDFBibTeX XMLCite \textit{K. Toyonaga}, J. Comput. Appl. Math. 199, No. 2, 432--436 (2007; Zbl 1112.65032) Full Text: DOI
Becuwe, Stefan; Cuyt, Annie On the fast solution of Toeplitz-block linear systems arising in multivariate approximation theory. (English) Zbl 1106.65023 Numer. Algorithms 43, No. 1, 1-24 (2006). MSC: 65F05 15A23 41A21 65G20 65G30 PDFBibTeX XMLCite \textit{S. Becuwe} and \textit{A. Cuyt}, Numer. Algorithms 43, No. 1, 1--24 (2006; Zbl 1106.65023) Full Text: DOI
Rump, S. M. Verification of positive definiteness. (English) Zbl 1101.65039 BIT 46, No. 2, 433-452 (2006). Reviewer: Petko Hr. Petkov (Sofia) MSC: 65F15 65G20 15B48 65G50 PDFBibTeX XMLCite \textit{S. M. Rump}, BIT 46, No. 2, 433--452 (2006; Zbl 1101.65039) Full Text: DOI
Rump, Siegfried M. Eigenvalues, pseudospectrum and structured perturbations. (English) Zbl 1093.15020 Linear Algebra Appl. 413, No. 2-3, 567-593 (2006). Reviewer: Ching-Hua Chang (Hualien) MSC: 15A42 65F15 15B57 15A12 PDFBibTeX XMLCite \textit{S. M. Rump}, Linear Algebra Appl. 413, No. 2--3, 567--593 (2006; Zbl 1093.15020) Full Text: DOI
Malyshev, A. N.; Sadkane, M. Componentwise pseudospectrum of a matrix. (English) Zbl 1050.15009 Linear Algebra Appl. 378, 283-288 (2004). Reviewer: Ralf Gramlich (Darmstadt) MSC: 15A18 PDFBibTeX XMLCite \textit{A. N. Malyshev} and \textit{M. Sadkane}, Linear Algebra Appl. 378, 283--288 (2004; Zbl 1050.15009) Full Text: DOI
Rump, Siegfried M.; Zemke, Jens-Peter M. On eigenvector bounds. (English) Zbl 1042.65029 BIT 43, No. 4, 823-837 (2003). Reviewer: Amin Boumenir (Carrollton) MSC: 65F15 15A42 PDFBibTeX XMLCite \textit{S. M. Rump} and \textit{J.-P. M. Zemke}, BIT 43, No. 4, 823--837 (2003; Zbl 1042.65029) Full Text: DOI
Huhtanen, Marko; Larsen, Rasmus Munk Exclusion and inclusion regions for the eigenvalues of a normal matrix. (English) Zbl 1029.65034 SIAM J. Matrix Anal. Appl. 23, No. 4, 1070-1091 (2002). Reviewer: E.Kreyszig (Ottawa) MSC: 65F15 15A42 PDFBibTeX XMLCite \textit{M. Huhtanen} and \textit{R. M. Larsen}, SIAM J. Matrix Anal. Appl. 23, No. 4, 1070--1091 (2002; Zbl 1029.65034) Full Text: DOI