Topological complexity of zero finding with algebraic operations
How many tests does one have to perform in order to compute an epsilon-approximation of a zero of a function f out of a given class of continuous functions on the unit interval, for a given epsilon > 0? We study this question in the context of the real number oracle machine model which uses the four standard arithmetic operations, comparisons with zero, and function values at adaptively chosen points. Let 0  0 one needs exactly [log(2)(1/(2epsilon))] tests in the worst case during a computation. For the subclass of all functions which are additionally nondecreasing one needs roughly log(2) log(2) epsilon(-1) tests, and for the subclass of all functions which are additionally increasing one needs exactly 1 test. (C) 2002 Elsevier Science (USA).
topological complexity zero finding algebraic operations oracle machine over the real numbers information-based complexity