Optimal Oscillation Points for Polynomials of Restricted Growth on the Real Line
نویسنده
چکیده
Computational methods are given in [3] to determine the maximum possible absolute value of each of the coe cients of the polynomials in this class when satis es some restrictions. It is also shown that there exist polynomials P and Q in the class such that each of the nonzero coe cients of P and Q have the largest possible absolute value of any polynomial in the class. The extremal polynomials P and Q are of degrees m 1 andm, respectively, with one of the polynomials even and the other odd. Together their coe cients give the best estimates on the absolute values of all of the coe cients of polynomials in the class. Each of the polynomials P and Q is characterized by a decreasing sequence of points x1; : : : ; xm and y1; : : : ; ym 1, respectively, where equality holds in the inequalities
منابع مشابه
A two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملA spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems
In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature fo...
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملOn-Line Learning of a Persian Spoken Dialogue System Using Real Training Data
The first spoken dialogue system developed for the Persian language is introduced. This is a ticket reservation system with Persian ASR and NLU modules. The focus of the paper is on learning the dialogue management module. In this work, real on-line training data are used during the learning process. For on-line learning, the effect of the variations of discount factor (g) on the learning speed...
متن کاملOn-Line Learning of a Persian Spoken Dialogue System Using Real Training Data
The first spoken dialogue system developed for the Persian language is introduced. This is a ticket reservation system with Persian ASR and NLU modules. The focus of the paper is on learning the dialogue management module. In this work, real on-line training data are used during the learning process. For on-line learning, the effect of the variations of discount factor (g) on the learning speed...
متن کامل