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On the Role of Computable Error Estimates in the Analysis of Numerical Approximation Algorithms

In: From Topology to Computation: Proceedings of the Smalefest

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  • Feng Gao

Abstract

Truncation error estimation for methods of numerical approximation, i.e., estimation of their errors of approximation, is an important constituent of numerical analysis. The error estimates obtained can be dichotomized according to whether an error estimate is computable from information that can be used for computing the approximations. For example, the standard error estimate for the bisection method for finding a zero of a function f(x) in an interval [a, b], under the assumption that f is continuous on [a, b] with f(a)f(b)

Suggested Citation

  • Feng Gao, 1993. "On the Role of Computable Error Estimates in the Analysis of Numerical Approximation Algorithms," Springer Books, in: Morris W. Hirsch & Jerrold E. Marsden & Michael Shub (ed.), From Topology to Computation: Proceedings of the Smalefest, chapter 36, pages 387-394, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2740-3_36
    DOI: 10.1007/978-1-4612-2740-3_36
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