Checking If There Exists a Monotonic Function That Is Consistent with the Measurements: An Efficient Algorithm

Checking If There Exists a Monotonic Function That Is Consistent with the Measurements: An... 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 x i and y = f(x) have been made, and we want to check whether the results of these measurements are consistent with the monotonicity of f(x). An efficient parallelizable algorithm is known for solving this problem when the values x i are known precisely, while the values y i are known with interval uncertainty. In this paper, we extend this algorithm to a more general (and more realistic) situation when both x i and y i are known with interval uncertainty. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Checking If There Exists a Monotonic Function That Is Consistent with the Measurements: An Efficient Algorithm

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Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer Science + Business Media, Inc.
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-005-6892-x
Publisher site
See Article on Publisher Site

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 x i and y = f(x) have been made, and we want to check whether the results of these measurements are consistent with the monotonicity of f(x). An efficient parallelizable algorithm is known for solving this problem when the values x i are known precisely, while the values y i are known with interval uncertainty. In this paper, we extend this algorithm to a more general (and more realistic) situation when both x i and y i are known with interval uncertainty.

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2005

References

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