A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations
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
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Chandrasekaran, S., & Sayed, A. H. (1998). A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations. SIAM Journal on Matrix Analysis and Applications, 19(1), 107–139. https://doi.org/10.1137/S0895479895296458
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1998
19
1
107
139
REVIEWED
OTHER