A note on downdating the Cholesky factorization
SIAM Journal on Scientific and Statistical Computing
Fast parallel algorithms for QR and triangular factorization
SIAM Journal on Scientific and Statistical Computing
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Generalized Displacement Structure for Block-Toeplitz,Toeplitz-Block, and Toeplitz-Derived Matrices
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
Stabilizing the Generalized Schur Algorithm
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Stability Issues in the Factorization of Structured Matrices
SIAM Journal on Matrix Analysis and Applications
A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations
SIAM Journal on Matrix Analysis and Applications
Displacement structure and array algorithms
Fast reliable algorithms for matrices with structure
Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem
SIAM Journal on Matrix Analysis and Applications
Fast robust regression algorithms for problems with Toeplitz structure
Computational Statistics & Data Analysis
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The generalized Schur algorithm (GSA) is a fast method to compute the Cholesky factorization of a wide variety of structured matrices. The stability property of the GSA depends on the way it is implemented. In [15] GSA was shown to be as stable as the Schur algorithm, provided one hyperbolic rotation in factored form [3] is performed at each iteration. Fast and efficient algorithms for solving Structured Total Least Squares problems [14,15] are based on a particular implementation of GSA requiring two hyperbolic transformations at each iteration. In this paper the authors prove the stability property of such implementation provided the hyperbolic transformations are performed in factored form [3].