Abstract
We describe symmetric positive definite Toeplitz systems for which the floating point vector that is closest to the actual solution is not the solution of a nearby symmetric Toeplitz system. With these systems we are able to show that a large class of Toeplitz solvers are not strongly stable for solving symmetric (or symmetric positive definite) Toeplitz systems; i.e., the computed solution is not necessarily the solution of a nearby symmetric Toeplitz system. This class of algorithms includes Gaussian elimination and seems to include all known fast and superfast Toeplitz solvers; certainly, it includes the better known ones. These results strongly suggest that all symmetric Toeplitz solvers are not strongly stable.
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© 1992 Springer-Verlag Berlin Heidelberg
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Linzer, E. (1992). Can symmetric Toeplitz solvers be strongly stable?. In: Dolev, D., Galil, Z., Rodeh, M. (eds) Theory of Computing and Systems. ISTCS 1992. Lecture Notes in Computer Science, vol 601. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035173
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DOI: https://doi.org/10.1007/BFb0035173
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