The refined harmonic Arnoldi method and an implicitly restarted refined algorithm for computing interior eigenpairs of large matrices
The author proposes a new variant of the implicitly restarted Arnoldi algorithm, called the implicitly restarted refined harmonic Arnoldi algorithm (IRRHA-adding one more acronym to the long list of Krylov subspace methods). It is suited to find interior eigenvalues when a shift and invert strategy is deemed as unfeasible. The use of refined shifts (which are better approximations to eigenvalues than the not-refined ones) is responsible for the superior performance. This is motivated by an interesting theorem, which suggest that in exact arithmetic the exact eigenvalues can be found with a small number of restarts. The paper concludes with numerical examples and tests which show the superior performance of the new algorithm.
scientific article; zbMATH DE number 1879059