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We propose a Preconditioned Locally Harmonic Residual (PLHR) method forcomputing several interior eigenpairs of a generalized Hermitian eigenvalueproblem, without traditional spectral transformations, matrix factorizations,or inversions. PLHR is based on a short-term recurrence, easily extended to ablock form, computing eigenpairs simultaneously. PLHR can take advantage ofHermitian positive definite preconditioning, e.g., based on an approximateinverse of an absolute value of a shifted matrix, introduced in [SISC, 35(2013), pp. A696-A718]. Our numerical experiments demonstrate that PLHR isefficient and robust for certain classes of large-scale interior eigenvalueproblems, involving Laplacian and Hamiltonian operators, especially if memoryrequirements are tight.

Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices