Checking if There Exists a Monotonic Function That is Consistent with the Measurements: An Efficient Algorithm

Authors

Kavitha Tupelly
Vladik Kreinovich, The University of Texas at El PasoFollow
Karen Villaverde

Publication Date

11-2004

Comments

UTEP-CS-04-19a.

Published in Reliable Computing, 2005, Vol. 11, No. 4, pp. 291-312.

Abstract

In many problems in science and engineering ranging from astrophysics to geosciences to financial analysis, we know that a physical quantity y depends on the physical quantity x, i.e., y=f(x) for some function f(x), and we want to check whether this dependence is monotonic. Specifically, finitely many measurements of xi and yi=f(xi) have been made, and we want to check whether the results of these measurements are consistent with the monotonicity of f. An efficient parallelizable algorithm is known for solving this problem when the values xi are known precisely, while the values yi are known with interval uncertainty. In this paper, we extend this algorithm to a more general (and more realistic) situation when both xi and yi are known with interval uncertainty.