On local quadratic convergence of inexact simplified Jacobi–Davidson method for interior eigenpairs of Hermitian eigenproblems

Abstract

For the Hermitian eigenproblems, under proper assumption on an initial approximation to the desired eigenvector, we prove local quadratic convergence of the inexact simplified Jacobi–Davidson method when the involved relaxed correction equation is solved by a standard Krylov subspace iteration, which particularly leads to local cubic convergence when the relaxed correction equation is solved to a prescribed precision proportional to the norm of the current residual. These results are valid for the interior as well as the extreme eigenpairs of the Hermitian eigenproblem and, hence, generalize the results by Bai and Miao (2017) from the extreme eigenpairs to the interior ones.