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We start with the positive definite Toeplitz matrix

By Michael Stewart


This paper describes a new O(n log 3 (n)) solver for the positive definite Toeplitz system T x = b. Instead of computing generators for the inverse of T, the new algorithm adjoins b to T and applies a superfast Schur algorithm to the resulting augmented matrix. The generators of this augmented matrix and its Schur complements are used by a divide-and-conquer block back-substitution routine to complete the solution of the system. The goal is to avoid the well-known numerical instability inherent in explicit inversion. Experiments suggest that the algorithm is backward stable in most cases

Year: 2003
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