Low Rank Approximation of a Hankel Matrix by Structured Total Least Norm

Abstract

The structure preserving rank reduction problem arises in many important applications. The singular value decomposition (SVD), while giving the best low rank approximation to a given matrix, 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 matri.x, which is based on Structured Total Least Norm (STLN). The STLN is an efficient method for obtaining an approximate solution to the overdetermined linear system AX ~ B preserving the given linear structure in .4. or (A I BJ, where errors can occur in both the right hand side matrix B and the matrix A. The approximate solution can be obtained to minimize the error in the Lp norm, where p = l, 2, or oo. An algorithm is described for Hankel structure preserving low rank approximation using STLN with Lp norm. Computational results are presented, which compare performances of the STLN based method for L1 and L2 norms and other existing methods for reduced rank approximation for Hankel matrices.