Displaying similar documents to “NP-Hard Problems and Test Problems For Global Concave Minimization Methods”

Polynomials over the reals in proofs of termination : from theory to practice

Salvador Lucas (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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This paper provides a framework to address termination problems in term rewriting by using orderings induced by algebras over the reals. The generation of such orderings is parameterized by concrete monotonicity requirements which are connected with different classes of termination problems: termination of rewriting, termination of rewriting by using dependency pairs, termination of innermost rewriting, top-termination of infinitary rewriting, termination of context-sensitive rewriting,...

On the Łojasiewicz exponent at infinity of real polynomials

Ha Huy Vui, Pham Tien Son (2008)

Annales Polonici Mathematici

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Let f: ℝⁿ → ℝ be a nonconstant polynomial function. Using the information from the "curve of tangency" of f, we provide a method to determine the Łojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Łojasiewicz exponent at infinity is finite or not. Then we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Łojasiewicz exponent at infinity of f and the problem of...

Intersect a quartic to extract its roots

Raghavendra G. Kulkarni (2017)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one...