On the Stability of the Generalized Schur Algorithm
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Journal of VLSI Signal Processing Systems
An Efficient Parallel Algorithm to Solve Block-Toeplitz Systems
The Journal of Supercomputing
A lanczos-type algorithm for the QR factorization of cauchy-like matrices
Contemporary mathematics
A displacement approach to decoding algebraic codes
Contemporary mathematics
An efficient circulant MIMO equalizer for CDMA downlink: algorithm and VLSI architecture
EURASIP Journal on Applied Signal Processing
On the computation of the rank of block bidiagonal Toeplitz matrices
Journal of Computational and Applied Mathematics
IEEE Transactions on Wireless Communications
A fast solver for linear systems with displacement structure
Numerical Algorithms
Parallel QR processing of Generalized Sylvester matrices
Theoretical Computer Science
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The concept of displacement structure has been used to solve several problems connected with Toeplitz matrices and with matrices obtained in some way from Toeplitz matrices (e.g., by combinations of multiplication, inversion, and factorization). Matrices of the latter type will be called Toeplitz-derived (or Toeplitz-like, close-to-Toeplitz). This paper introduces a generalized definition of displacement for block-Toeplitz and Toeplitz-block arrays. It will turn out that Toeplitz-derived matrices are perhaps best regarded as particular Schur complements obtained from suitably defined block matrices. The new displacement structure is used to obtain a generalized Schur algorithm for fast triangular and orthogonal factorizations of all such matrices and well-structured fast solutions of the corresponding exact and overdetermined systems of linear equations. Furthermore, this approach gives a natural generalization of the so-called Gohberg-Semencul formulas for Toeplitz- derived matrices.