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Chebyshev's sum inequality, about sums and products of decreasing sequences Chebyshev's equioscillation theorem , on the approximation of continuous functions with polynomials The statement that if the function π ( x ) ln x / x {\textstyle \pi (x)\ln x/x} has a limit at infinity, then the limit is 1 (where π is the prime-counting function).
It runs in polynomial time on inputs that are in SUBSET-SUM if and only if P = NP: // Algorithm that accepts the NP-complete language SUBSET-SUM. // // this is a polynomial-time algorithm if and only if P = NP. // // "Polynomial-time" means it returns "yes" in polynomial time when // the answer should be "yes", and runs forever when it is "no".
In the balanced assignment problem, both parts of the bipartite graph have the same number of vertices, denoted by n. One of the first polynomial-time algorithms for balanced assignment was the Hungarian algorithm. It is a global algorithm – it is based on improving a matching along augmenting paths (alternating paths between unmatched vertices
Worse still, it is APX-complete, meaning there is no polynomial-time approximation scheme (PTAS) for this problem unless P=NP. WMSAT is the problem of finding an assignment of minimum weight that satisfy a monotone Boolean formula (i.e. a formula without any negation). Weights of propositional variables are given in the input of the problem.
In mathematics, Turán's inequalities are some inequalities for Legendre polynomials found by Pál Turán (and first published by Szegö (1948)). There are many generalizations to other polynomials, often called Turán's inequalities, given by (E. F. Beckenbach, W. Seidel & Otto Szász 1951 ) and other authors.
In approximation theory, Jackson's inequality is an inequality bounding the value of function's best approximation by algebraic or trigonometric polynomials in terms of the modulus of continuity or modulus of smoothness of the function or of its derivatives. [1]
Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. [8] For higher degrees, the specific names are not commonly used, although quartic polynomial (for degree four) and quintic polynomial (for degree five) are sometimes used. The names for the degrees may be applied to the ...
In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if ...
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