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The SUFFICIENT-POINTS 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 design use of a class of mathematical operations. These operations 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 other variable that is “sufficient” in this sense. Suppose that ◯ is an interval of input vectors, and  an interval matrix. Then, one Sufficient-Points operation returns a set of vectors ~ such that for each b in ~, the set of x values that can be produced by inserting all the values of  into Ax = b is a superset of the input vector x. These operations have been partly overlooked by the interval matrix mathematics community, but are mathematically interesting and useful in the design, for example, of circuits.

Keywords

Set-Based DesignFinite ElementsInterval MatricesInternal VectorDesign Compiler
Type
Articles
Information
AI EDAM , Volume 9 , Issue 3 , June 1995 , pp. 211 - 217
Copyright
Copyright © Cambridge University Press 1995

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References

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