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This paper proposes a harmonic Lanczos bidiagonalization method for computingsome interior singular triplets of large matrices. It is shown that theapproximate singular triplets are convergent if a certain Rayleigh quotientmatrix is uniformly bounded and the approximate singular values are wellseparated. Combining with the implicit restarting technique, we develop animplicitly restarted harmonic Lanczos bidiagonalization algorithm and suggest aselection strategy of shifts. Numerical experiments show that one can use thisalgorithm to compute interior singular triplets efficiently.

A harmonic Lanczos bidiagonalization method for computing interior singular triplets of large matrices