Method of Bounds
Algorithm 1.2 is an approximate dependence algorithm that checks if (1) the system of dependence equations has an integer solution, and (2) the combined system of equations and inequalities has a real solution. The method of bounds is an implementation of Algorithm 1.2 that consists of two major tests: the generalized gcd test to check for an integer solution to the equations, and the bounds test to check for a real solution to the equations and the inequalities. We covered the first test in Section 5.4; this chapter is devoted to the second. For this chapter, we need several mathematical definitions and results that have been collected in the appendix.
KeywordsDirection Vector Real Solution Integer Solution Integer Variable Loop Nest
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