Efficient Parameter Estimation and Implementation of a Contour Integral-Based Eigensolver

We consider an eigensolver for computing eigenvalues in a given domain and the corresponding eigenvectors of large-scale matrix pencils. The Sakurai-Sugiura (SS) method is an eigensolver based on complex moments given by contour integrals of matrix inverses with several shift points. This method has good parallel scalability, and is suitable for massively parallel computing environments. The SS method has several parameters, and the choice of these parameters is crucial for achieving high accuracy and good parallel performance. We discuss some numerical properties of the method, and present efficient parameter estimation techniques. We demonstrate the efficiency of our method with numerical experiments.