A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations

Authors:
S. Chandrasekaran;Ali H. Sayed
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1998

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Abstract

We derive a stable and fast solver for nonsymmetric linear systems of equations with shift structured coefficient matrices (e.g., Toeplitz, quasi-Toeplitz, and product of two Toeplitz matrices). The algorithm is based on a modified fast QR factorization of the coefficient matrix and relies on a stabilized version of the generalized Schur algorithm for matrices with displacement structure. All computations can be done in O(n2) operations, where n is the matrix dimension, and the algorithm is backward stable.