Backward Error Estimates for Toeplitz Systems
- 1 April 1994
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 15 (2), 408-417
- https://doi.org/10.1137/S0895479891219976
Abstract
Given a computed approximate solution $\bar x$ to $Ax = b$, it is interesting to find nearby systems with $\bar x$ as exact solution and that have the same structure as A. This paper shows that the distance to these nearby structured systems can be much larger than for the corresponding general perturbation for general and symmetric Toeplitz systems. In fact, even the correctly rounded solution $\hat x$ may require a structured perturbation with terms as large as $\| \hat x \|$ times the machine precision.
Keywords
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