A Lanczos bidiagonalization algorithm for Hankel matrices

This paper presents a fast algorithm for bidiagonalizing a Hankel matrix. An m×n Hankel matrix is reduced to a real bidiagonal matrix in O((m+n)nlog(m+n)) floating-point operations (flops) using the Lanczos method with modified partial orthogonalization and reset schemes to improve its stability. Performance improvement is achieved by exploiting the Hankel structure, as fast Hankel matrix–vector multiplication is used. The accuracy and efficiency of the algorithm are demonstrated by our numerical experiments.