A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error-Reference-Cited by-同舟云学术

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A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error

Published:2018-07-25 Issue:3 Volume:55 Page:
ISSN:0008-0624
Container-title:Calcolo
language:en
Short-container-title:Calcolo

Author:

Bueno M. I.,Dopico F. M.,Furtado S.,Medina L.

Funder

National Science Foundation

Ministerio de Economía y Competitividad

Publisher

Springer Science and Business Media LLC

Subject

Computational Mathematics,Algebra and Number Theory

Link

http://link.springer.com/article/10.1007/s10092-018-0273-4/fulltext.html

Reference44 articles.

1. Adhikari, B., Alam, R., Kressner, D.: Structured eigenvalue condition numbers and linearizations for matrix polynomials. Linear Algebra Appl. 435, 2193–2221 (2011)

2. Al-Ammari, M., Tisseur, F.: Hermitian matrix polynomials with real eigenvalues of definite type. Part I: classification. Linear Algebra Appl. 436, 3954–3973 (2012)

3. Antoniou, E.N., Vologiannidis, S.: A new family of companion forms of polynomial matrices. Electron. J. Linear Algebra 11, 78–87 (2004)

4. Betcke, T., Higham, N. J., Mehrmann, V., Schröder, C., Tisseur, F.: NLEVP: a collection of nonlinear eigenvalue problems. ACM Trans. Math. Softw. 39(2), 7:1–7:28 (2013)

5. Bini, D.A., Gemignani, L., Tisseur, F.: The Ehrlich–Aberth method for the nonsymmetric tridiagonal eigenvalue problem. SIAM J. Matrix Anal. Appl. 27, 153–175 (2005)

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2. The infinite Lanczos method for symmetric nonlinear eigenvalue problems;Calcolo;2023-03-05

3. On why using $${{\mathbb {D}}}{{\mathbb {L}}}(P)$$ for the symmetric polynomial eigenvalue problem might need to be reconsidered;Calcolo;2022-11

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5. Backward error and conditioning of Fiedler companion linearizations;Mathematics of Computation;2019-10-17

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