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On a modification of the EVEN‐IRA algorithm for the solution of T ‐even polynomial eigenvalue problems
Author(s) -
Faßbender Heike,
Saltenberger Philip
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800006
Subject(s) - eigenvalues and eigenvectors , polynomial , mathematics , algorithm , linearization , spectrum (functional analysis) , divide and conquer eigenvalue algorithm , matrix polynomial , discrete mathematics , nonlinear system , mathematical analysis , physics , quantum mechanics
We discuss the numerical solution of T ‐even n × n polynomial eigenvalue problems and show how a small portion of the spectrum can be obtained using just ( n 3 ) arithmetic operations. For that purpose, we apply the EVEN‐IRA algorithm proposed in [1] to a special structure‐preserving linearization. In this particular situation, the Arnolid iteration as a main part of the EVEN‐IRA algorithm can be realized very efficiently.