Numerical analysis and its applications vol:1988 pages:560-567
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  GSA was shown to be as stable as the Schur algorithm, provided one hyperbolic rotation in factored form  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 .