On the Cost of Uniform and Nonuniform Algorithms

Erich Novak, Henryk Wozniakowski

September 1997, April 1998

We compare the costs of uniform and nonuniform algorithms for approximate solutions of continuous problems assuming the real number model. We show that, in general, there is no relation between them. That is, the class of uniform algorithms may be empty, and if this class is non-empty then the cost of any uniform algorithm may be arbitrarily larger than the minimal cost of nonuniform algorithms. We also provide conditions under which there exist uniform algorithms whose cost is basically the same as the minimal cost of nonuniform algorithms.

The paper will appear in Th. Comp. Sci.