A new graph characteristic and its application to numerical computability

Many traditional numerical algorithms include a step on which we check whet her a given real number a is equal to 0. This checking is easy for rational numbers, but for constructive real numbers, whether a number is 0 or not i s an algorithmically undecidable problem. It is therefore desirable to re-f ormulate the existing algorithms with as few such comparisons as possible. We describe a new graph characteristic; this characteristic describes how t he number of comparisons in an algorithm can be reduced. (C) 2001 Elsevier Science B.V. All rights reserved.