Rounding errors of partial derivatives of simple eigenvalues of the quadratic eigenvalue problem

Xin Lu ^[1] ; Shufang Xu ^[2]
1. [1] Institute of Applied Physics and Computational Mathematics
  
  Institute of Applied Physics and Computational Mathematics
  
  China
2. [2] Peking University
  
  Peking University
  
  China
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 282, Nº 1 (July 2015), 2015, págs. 268-277
Idioma: inglés
DOI: 10.1016/j.cam.2014.12.046
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Resumen
- In this paper, we derive rounding errors of partial derivatives of a simple eigenvalue of the quadratic eigenvalue problem dependent on several parameters. We prove a series of lemmas and finally get theorems of rounding errors of both nonsymmetric and symmetric QEPs. Examples are given to show the validity of our theorems, and numerical results show that our rounding error is a very good upper bound estimation of the relative error of the eigenvalue.