Basic Problem of Interval Computations for Polynomials of a Fixed Number of Variables
In the previous chapter, we proved that the problem of computing the range f(x1,..., xn) of a given polynomial f(x1,..., xn) over given intervals x1,..., xn is, in general, computationally intractable (NP-hard). Since this general problem is intractable, it is desirable to look for cases in which it is feasible. In this chapter, we analyze what happens when we restrict the number of variables n. Good news is that in this case, a polynomial-time algorithm is possible. Bad news is that the existing polynomial-time algorithms require too much computation time to be practical.
KeywordsPolynomial Time Rational Number Algebraic Function Exponential Time Computational Step
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