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The feasible regions of linear programming are defined by a set of inequalities. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [1] It is used most often to compare two numbers on the number line by their size.
The rational univariate representation or RUR is a representation of the solutions of a zero-dimensional polynomial system over the rational numbers which has been introduced by F. Rouillier. [10] A RUR of a zero-dimensional system consists in a linear combination x 0 of the variables, called separating variable, and a system of equations [11]
Every Laurent polynomial can be written as a rational function while the converse is not necessarily true, i.e., the ring of Laurent polynomials is a subring of the rational functions. The rational function () = is equal to 1 for all x except 0, where there is a removable singularity. The sum, product, or quotient (excepting division by the ...
In algebra, a Landau-Mignotte bound (sometimes only referred to as Mignotte's bound [1]) is one of a family of inequalities concerning a univariate integer polynomial f(x) and one of its factors h(x).
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 ...
A polynomial function is one that has the form = + + + + + where n is a non-negative integer that defines the degree of the polynomial. A polynomial with a degree of 0 is simply a constant function; with a degree of 1 is a line; with a degree of 2 is a quadratic; with a degree of 3 is a cubic, and so on.
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]
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution