On the cost of uniform and nonuniform algorithms

We compare the costs of uniform and nonuniform algorithms for approximate s olutions of continuous problems assuming the real number model. We show tha t, in general, there is no relation between these costs. That is, the class of uniform algorithms may be empty; moreover, even if this class is nonemp ty then the cost of any uniform algorithm may be arbitrarily larger than th e minimal cost of nonuniform algorithms. We also provide conditions under w hich there exist uniform algorithms whose cost is basically the same as the minimal cost of nonuniform algorithms. (C) 1999 Elsevier Science B.V. All rights reserved.