Abstract
We show how to stabilize the generalized Schur algorithm for the Cholesky factorization of positive-definite structured matrices R that satisfy R-FRF T = GJG T , where J is a signature matrix, F is a stable lower-triangular matrix, and G is a generator matrix. We use a perturbation analysis to indicate the best accuracy that can be expected from any finite precision algorithm that uses the generator matrix as the input data. We then show that the modified Schur algorithm proposed in this work essentially achieves this bound for a large class of structured matrices.
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