Naslov
An algorithm for the solution of quartic eigenvalue problems

Autori
Šain Glibić, Ivana

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
ApplMath18 - Ninth Conference on Applied Mathematics and Scientific Computing

Mjesto i datum
Šibenik, Hrvatska, 17.09.2018. - 20.09.2018

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
eigenvalues ; quartic eigenvalue problem ; QR factorization ; QZ method ; backward error ; infinite eigenvalues

Sažetak
Quartic eigenvalue problem appears in a variety of applications, e.g. calibration of the central catadioptric vision system and spatial stability analysis of the Orr Sommerfeld equation. The standard approach for solving the polynomial eigenvalue problem is to linearize it, and then use the QZ algorithm to solve corresponding generalized eigenvalue problem. However, De Teran, Dopico and Mackey developed equivalence relation, so called quadratification, that converts quartic eigenvalue problem into an equivalent quadratic eigenvalue problem. Hammarling, Munro, and Tisseur developed the algorithm for the complete solution of this problem: quadeig. We analyse numerical properties of the quadeig algorithm when used for solving the quartic eigenvalue problem. We propose modifications in two key segments of the algorithm: scaling and deflation of zero and infinite eigenvalues. Specifically, we use the structure of the quadratification for rank determination of coefficient matrices, which is the main part of deflation process. In addition, we determine the test for the existence of Jordan blocks for infinite and zero eigenvalues in terms of the original quartic problem. Finally, we provide numerical examples to illustrate the power of the proposed algorithm.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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