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The SUFFICIENT-POINTS family of propagation operations for intervals on simultaneous linear equations
R. Chen, A.C. Ward
Journal:

AI EDAM / Volume 9 / Issue 3 / June 1995

Published online by Cambridge University Press:

27 February 2009, pp. 211-217
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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 Â 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 Â 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.