The Jacobi-Davidson method for eigenvalue problems as an accelerated inexact Newton scheme

Abstract

We discuss a new method for the iterative computation of a portion of the spectrum of a large sparse matrix. The matrix may be complex and non-normal. The method also delivers the Schur vectors associated with the computed eigenvalues. The eigenvectors can easily be computed from the Schur vectors, and for stability reasons we prefer the approach with Schur vectors. The method is based on the recently introduced Jacobi-Davidson algorithm [16]. This method improves the Davidson method and its generalizations. We also show how the Davidson's methods, including the new one, can be viewed as accelerated inexact Newton schemes.