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}
}
  • M. Stewart
  • Published 1 March 2003
  • Computer Science
  • SIAM J. Matrix Anal. Appl.
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… 

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