Asymptotic Optimality of the Bisection Method

Sikorski, Krzysztof A.; Trojan, G. M.

The bisection method is shown to possess the asymptotically best rate of convergence for infinitely differentiable functions having zeros of arbitrary multiplicity. If the multiplicity of zeros is bounded methods are known which have asymptotically at least quadratic rate of convergence.


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Academic Units
Computer Science
Department of Computer Science, Columbia University
Columbia University Computer Science Technical Reports, CUCS-092-84
Published Here
October 26, 2011