  This paper proposes a harmonic Lanczos bidiagonalization method for computing
some interior singular triplets of large matrices. It is shown that the
approximate singular triplets are convergent if a certain Rayleigh quotient
matrix is uniformly bounded and the approximate singular values are well
separated. Combining with the implicit restarting technique, we develop an
implicitly restarted harmonic Lanczos bidiagonalization algorithm and suggest a
selection strategy of shifts. Numerical experiments show that one can use this
algorithm to compute interior singular triplets efficiently.
