Stability of Levinson algorithm for Toeplitz-like systems

Numerical stability of the Levinson algorithm generalized for Toeplitzlike systems, is studied. Arguments based on the analytic results of an error analysis for floating point arithmetic produce an exponential upper bound on the norm of the residual vector. The base of such exponential function can be small for a class of matrices containing point row diagonally dominant matrices. Numerical experiments show that, for this class, Gaussian elimination by row and Levinson algorithm have residuals of the same order of magnitude. As expected, the empirical results point out that the theoretical bound is too pessimistic