polynomial inequality

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• Polynomial SOS — In mathematics, a homogeneous form h ( x ) of degree 2 m in the real n dimensional vector x is a SOS (sum of squares) of homogeneous forms if and only if it can be written as a sum of squares of homogeneous forms of degree m ::h(x) mbox{is SOS}… …   Wikipedia

• Bernstein's inequality (mathematical analysis) — In the mathematical theory of mathematical analysis, Bernstein s inequality, named after Sergei Natanovich Bernstein, is defined as follows.Let P be a polynomial of degree n with derivative P prime; . Then:max(P ) le ncdotmax(P) where we define… …   Wikipedia

• Properties of polynomial roots — In mathematics, a polynomial is a function of the form: p(x) = a 0 + a 1 x + cdots a n x^n, quad xin mathbb{C}where the coefficients a 0, ldots, a n are complex numbers. The fundamental theorem of algebrastates that polynomial p has n roots. The… …   Wikipedia

• Markov brothers' inequality — In mathematics, the Markov brothers inequality is an inequality proved by Andrey Markov and Vladimir Markov. This inequality bounds the maximum of the derivatives of a polynomial on an interval in terms of the maximum of the polynomial.[1] For k …   Wikipedia

• Askey–Gasper inequality — In mathematics, the Askey–Gasper inequality, named after Richard Askey and George Gasper, is an inequality for Jacobi polynomials proved by harvtxt|Askey|Gasper|1976. It states that if beta; ge; 0, α + beta; ge; −2, and −1 le; x le; 1 then:sum {k …   Wikipedia

• Linear matrix inequality — In convex optimization, a linear matrix inequality (LMI) is an expression of the form: LMI(y):=A 0+y 1A 1+y 2A 2+cdots+y m A mgeq0,where * y= [y i,, i!=!1dots m] is a real vector, * A 0,, A 1,, A 2,,dots,A m are symmetric matrices in the subspace …   Wikipedia

• Von Neumann's inequality — In operator theory, von Neumann s inequality, due to John von Neumann, states that, for a contraction T acting on a Hilbert space and a polynomial p , then the norm of p ( T ) is bounded by the supremum of | p ( z )| for z in the unit disk. [… …   Wikipedia

• MacLaurin's inequality — In mathematics, MacLaurin s inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let a 1, a 2, ..., a n be positive real numbers, and for k = 1, 2, ..., n define the averages S k as follows …   Wikipedia

• Weyl's inequality — In mathematics, there are at least two results known as Weyl s inequality .Weyl s inequality in number theoryIn number theory, Weyl s inequality, named for Hermann Weyl, states that if M , N , a and q are integers, with a and q coprime, q > 0,… …   Wikipedia

• Remez inequality — In mathematics the Remez inequality, discovered by the Ukrainian mathematician E. J. Remez in 1936, gives a bound on the sup norms of certain polynomials, the bound being attained by the Chebyshev polynomials.The inequalityLet sigma; be an… …   Wikipedia

• Jackson's inequality — In approximation theory, Jackson s inequality is an inequality (proved by Dunham Jackson) between the value of function s best approximation by polynomials and the modulus of continuity of its derivatives. Here is one of the simple cases… …   Wikipedia