A New Graph Characteristic and its Application to Numerical Computability

Authors

Frank Harary
Vladik Kreinovich, The University of Texas at El PasoFollow
Luc Longpre, The University of Texas at El PasoFollow

Publication Date

5-2000

Comments

UTEP-CS-99-24a.

Published in Information Processing Letters, 2001, Vol. 77, No. 5-6, pp. 277-282.

Abstract

Many traditional numerical algorithms include a step on which we check whether 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 is an algorithmically undecidable problem. It is therefore desirable to re-formulate the existing algorithms with as few such comparisons as possible. We describe a new graph characteristic; this characteristic describes how the number of comparisons in an algorithm can be reduced.