# A Superfast Toeplitz Solver with Improved Numerical Stability

@article{Stewart2003AST, title={A Superfast Toeplitz Solver with Improved Numerical Stability}, author={Michael Stewart}, journal={SIAM J. Matrix Anal. Appl.}, year={2003}, volume={25}, pages={669-693} }

This paper describes a new O(n log3(n)) solver for the positive definite Toeplitz system Tx=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…

## 37 Citations

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