An invert-free Arnoldi method for computing interior eigenpairs of large matrices

This paper presents an invert-free Arnoldi method for extracting a few interior eigenpairs of large sparse matrices. It is derived by implicitly applying the Arnoldi process with the shifted and inverted operator (A- I)-1 in a shifted Krylov subspace (A- I)Km(A, v1). Due to a subtle relationship between the Krylov subspace Km(A, v1) and its shifted Krylov subspace, we avoid forming the shifted and inverted operator explicitly. Comparisons are drawn between the harmonic Arnoldi method and the invert-free Arnoldi method. Finally, numerical results are reported to show the efficiency of the new method.