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The FEAST algorithm, due to Polizzi, is a typical contour-integral basedeigensolver for computing the eigenvalues, along with their eigenvectors,inside a given region in the complex plane. It was formulated under thecircumstance that the considered eigenproblem is Hermitian. The FEAST algorithmis stable and accurate, and has attracted much attention in recent years.However, it was observed that the FEAST algorithm may fail to find the targeteigenpairs when applying it to the non-Hermitian problems. Efforts have beenmade to adapt the FEAST algorithm to non-Hermitian cases. In this work, wedevelop a new non-Hermitian scheme for the FEAST algorithm. The mathematicalframework will be established, and the convergence analysis of our new methodwill be studied. Numerical experiments are reported to demonstrate theeffectiveness of our method and to validate the convergence properties.

A randomized FEAST algorithm for generalized eigenvalue problems