Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems
(2020) Linear Algebra and Its Applications — Vol. 604, p. 441-475 (2020)
Files
DopicoMQV20.pdf
Open Access - Adobe PDF
- 547.52 KB
Details
- Authors
Dopico, Froilán M. 
Marcaida, Silvia Quintana, María C.
- Abstract
- This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and poles in subsets of any algebraically closed field and also at infinity. This new theory of local linearizations captures and explains rigorously the properties of all the different pencils that have been used from the 1970's until 2020 for computing zeros, poles and eigenvalues of rational matrices. Particular attention is paid to those pencils that have appeared recently in the numerical solution of nonlinear eigenvalue problems through rational approximation.
- Affiliations
Citations
Dopico, F. M., Marcaida, S., Quintana, M. C., & Van Dooren, P. (2020). Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems. Linear Algebra and Its Applications, 604, 441-475. https://doi.org/10.1016/j.laa.2020.07.004 (Original work published 2020)