RT Journal Article
T1 Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems
A1 Martínez Dopico, Froilán César
A1 Marcaida, Silvia
A1 Quintana Ponce, María del Carmen
A1 Van Dooren, Paul
AB 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.
PB Elsevier
SN 0024-3795
YR 2020
FD 2020-11-01
LK https://hdl.handle.net/10016/32289
UL https://hdl.handle.net/10016/32289
LA eng
DS e-Archivo
RD 27 jul. 2024