A sinc-Gaussian technique for computing eigenvalues of second-order linear pencils

The sinc-Gaussian sampling technique derived by Qian (2002) establishes a sampling technique which converges faster than the classical sampling technique. Schmeisser and Stenger (2007) studied the associated error analysis. In the present paper we apply a sinc-Gaussian technique to compute the eigenvalues of a second-order operator pencil of the form Q − λ P approximately. Here Q and P are self-adjoint differential operators of the second and first order respectively. In addition, the eigenparameter appears in the boundary conditions linearly. The error of this method decays exponentially in terms of the number of involved samples. Therefore the accuracy of the new technique is higher than the classical sinc-method. This is confirmed via worked examples which are given at the end of the paper with comparisons with the classical sinc-method.