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

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.