Topological complexity of zero finding with algebraic operations

Authors:
Peter Hertling
Affiliations:
Theoretische Informatik I, Fernuniversität Hagen, 58084 Hagen, Germany
Venue:
Journal of Complexity
Year:
2002

Citing 5
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Abstract

How many tests does one have to perform in order to compute an ε-approximation of a zero of a function f out of a given class of continuous functions on the unit interval, for a given ε ε ½. We show that for the class of all continuous functions f on the unit interval with f(0) 0 and f(1) 2(1/(2ε))⌉ tests in the worst case during a computation. For the subclass of all functions which are additionally nondecreasing one needs roughly log2 log2 ε-1 tests, and for the subclass of all functions which are additionally increasing one needs exactly 1 test.