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The RANGE family of propagation operations for intervals on simultaneous linear equations

Published online by Cambridge University Press:  27 February 2009

R. Chen  and
A.C. Ward
R. Chen
Affiliation:
Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China
A.C. Ward
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109
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Abstract

Interval arithmetic has been extensively applied to systems of linear equations by the interval matrix arithmetic community. This paper demonstrates through simple examples that some of this work can be viewed as particular instantiations of an abstract “design operation,” the RANGE operation of the Labeled Interval Calculus formalism for inference about sets of possibilities in design. These particular operations promise to solve a variety of design problems that lay beyond the reach of the original Labeled Interval Calculus. However, the abstract view also leads to a new operation, apparently overlooked by the matrix mathematics community, that should also be useful in design; the paper provides an algorithm for computing it.

Keywords

Set-based DesignFinite ElementsInterval MatricesInterval VectorsDesign Compiler
Type
Articles
Information
AI EDAM , Volume 9 , Issue 3 , June 1995 , pp. 183 - 196
Copyright
Copyright © Cambridge University Press 1995

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