An invert-free Arnoldi method for computing interior eigenpairs of large matrices
Qiang Niu, Linzhang Lu · International Journal of Computer Mathematics · 2007
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−τ I)−1 in a shifted Krylov subspace (A−τ I)𝒦 m (A, v 1). Due to a subtle relationship between the Krylov subspace 𝒦 m (A, v 1) 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.