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An algorithm for the solution of quartic eigenvalue problems (CROSBI ID 698583)

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Šain Glibić, Ivana An algorithm for the solution of quartic eigenvalue problems // ApplMath18, Ninth conference on applied mathematics and scientific computing Šibenik, Hrvatska, 17.09.2018-20.09.2018

Podaci o odgovornosti

Šain Glibić, Ivana

engleski

An algorithm for the solution of quartic eigenvalue problems

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.

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

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Podaci o prilogu

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Podaci o skupu

ApplMath18, Ninth conference on applied mathematics and scientific computing

predavanje

17.09.2018-20.09.2018

Šibenik, Hrvatska

Povezanost rada

Matematika