Superfast solution of real positive definite toeplitz systems
SIAM Journal on Matrix Analysis and Applications
Toeplitz equations by conjugate gradients with circulant preconditioner
SIAM Journal on Scientific and Statistical Computing
Circulant preconditioners for Hermitian Toeplitz systems
SIAM Journal on Matrix Analysis and Applications
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Iterative solution methods
Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
SIAM Journal on Scientific Computing
New Band Toeplitz Preconditioners for Ill-Conditioned Symmetric Positive Definite Toeplitz Systems
SIAM Journal on Matrix Analysis and Applications
Preconditioners for Nondefinite Hermitian Toeplitz Systems
SIAM Journal on Matrix Analysis and Applications
Recursive-Based PCG Methods for Toeplitz Systems with Nonnegative Generating Functions
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
SIAM Journal on Matrix Analysis and Applications
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In this paper, we propose to solve the Toeplitz linear systems T n x驴=驴b by a recursive-based method. The method is based on repeatedly dividing the original problem into two subproblems that involve the solution of systems containing the Schur complement of the leading principal submatrix of the previous level. The idea is to solve the linear systems S m y驴=驴d, where S m is the Schur complement of T 2m (the principal submatrix of T n ), by using a self preconditioned iterative methods. The preconditioners, which are the approximate inverses of S m , are constructed based on famous Gohberg---Semencul formula. All occurring matrices are represented by proper generating vectors of their displacement rank characterization. We show that, for well conditioned problems, the proposed method is efficient and robust. For ill-conditioned problems, by using some iterative refinement method, the new method would be efficient and robust. Numerical experiments are presented to show the effectiveness of our new method.