Low rank approximation of a Hankel matrix by structured total least norm

The structure preserving rank reduction problem arises in many important applications. The singular value decomposition (SVD), while giving the closest low rank approximation to a given matrix in matrix L-2 norm and Frobenius norm, may not be appropriate for these applications since it does not preserve the given structure. We present a new method for structure preserving low rank approximation of a matrix, which is based on Structured Total Least Norm (STLN). The STLN is an efficient method for obtaining an approximate solution to an overdetermined linear system AX approximate to B, preserving the given linear structure in the perturbation [E F] such that (A + E)X = B + F. The approximate solution can be obtained to minimize the perturbation [E F] in the L-p norm, where p = 1, 2, or infinity. An algorithm is described for Hankel structure preserving low rank approximation using STLN with L-p norm. Computational results are presented, which show performances of the STLN based method for L-1 and L-2 norms for reduced rank approximation for Hankel matrices. AMS subject classification: 15A99, 65F20, 65F30.