A look-ahead Levinson algorithm for indefinite Toeplitz systems
SIAM Journal on Matrix Analysis and Applications
On the Stability of the Bareiss and Related Toeplitz Factorization Algorithms
SIAM Journal on Matrix Analysis and Applications
Displacement structure: theory and applications
SIAM Review
Matrix computations (3rd ed.)
Stability Issues in the Factorization of Structured Matrices
SIAM Journal on Matrix Analysis and Applications
Stable and Efficient Algorithms for Structured Systems of Linear Equations
SIAM Journal on Matrix Analysis and Applications
New Fast Algorithms for Structured Linear Least Squares Problems
SIAM Journal on Matrix Analysis and Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
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Numerical stability of the Levinson algorithm, generalized for Toeplitz-like systems, is studied. Arguments based on the analytic results of an error analysis for floating point arithmetic produce an upper bound on the norm of the residual vector, which grows exponentially with respect to the size of the problem. The base of such an exponential function can be small for diagonally dominant Toeplitz-like matrices. Numerical experiments show that, for these matrices, Gaussian elimination by row and the Levinson algorithm have residuals of the same order of magnitude. As expected, the empirical results point out that the theoretical bound is too pessimistic.