Divide and Conquer Algorithm for Toeplitz-like Systems: Stability analysis for the symmetric case

A superfast algorithm for the solution of Toeplitz-like systems has been introduced and tested in [4]. In this paper a theoretical error analysis of the algorithm is performed for the symmetric case. The analysis produces an upper bound to the norm of the residual vector, allowing the detection of some parameters which rule the stability behavior of the algorithm. These parameters take into account both the conditioning properties of the coefficient matrices at the different levels of recursion and the magnitude of some involved matrices measured through their generators. The experimentation confirms the theoretical results, pointing out that, in general, the upper bound to the norm of the residual vector is too pessimistic.