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The DOMAIN 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

This paper defines, develops algorithms for, and illustrates the utility in design of a class of mathematical operations. These accept as inputs a system of linear constraint equations, Ax = b, an interval matrix of values for the coefficients, A, and an interval vector of values for either x or b. They return a set of values for the “domain” of the other vector, in the sense that all combinations of the output vector values set and values for A, when inserted into the constraint equation, correspond to values for the input vector that lie within the input interval. These operations have been mostly overlooked by the interval matrix arithmetic community, but are mathematically interesting and useful in the design, for example, of structures.

Keywords

Set-Based DesignFinite ElementsInterval MatricesInterval VectorsDesign Compiler
Type
Articles
Information
AI EDAM , Volume 9 , Issue 3 , June 1995 , pp. 197 - 210
Copyright
Copyright © Cambridge University Press 1995

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References

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