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We introduce the Generalized Preconditioned Locally Harmonic Residual (GPLHR)method for solving standard and generalized non-Hermitian eigenproblems. Themethod is particularly useful for computing a subset of eigenvalues, and theireigen- or Schur vectors, closest to a given shift. The proposed method is basedon block iterations and can take advantage of a preconditioner if it isavailable. It does not need to perform exact shift-and-invert transformation.Standard and generalized eigenproblems are handled in a unified framework. Ournumerical experiments demonstrate that GPLHR is generally more robust andefficient than existing methods, especially if the available memory is limited.

Generalized preconditioned locally harmonic residual method for non-Hermitian eigenproblems