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Polynomial Approximation On Polytopes
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Book Synopsis Polynomial Approximation on Polytopes by : Vilmos Totik
Download or read book Polynomial Approximation on Polytopes written by Vilmos Totik and published by American Mathematical Soc.. This book was released on 2014-09-29 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial approximation on convex polytopes in is considered in uniform and -norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the -case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate -functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
Book Synopsis Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem by : David Handelman
Download or read book Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem written by David Handelman and published by Springer. This book was released on 1987 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emanating from the theory of C*-algebras and actions of tori theoren, the problems discussed here are outgrowths of random walk problems on lattices. An AGL (d,Z)-invariant (which is a partially ordered commutative algebra) is obtained for lattice polytopes (compact convex polytopes in Euclidean space whose vertices lie in Zd), and certain algebraic properties of the algebra are related to geometric properties of the polytope. There are also strong connections with convex analysis, Choquet theory, and reflection groups. This book serves as both an introduction to and a research monograph on the many interconnections between these topics, that arise out of questions of the following type: Let f be a (Laurent) polynomial in several real variables, and let P be a (Laurent) polynomial with only positive coefficients; decide under what circumstances there exists an integer n such that Pnf itself also has only positive coefficients. It is intended to reach and be of interest to a general mathematical audience as well as specialists in the areas mentioned.
Book Synopsis Introduction To The Theory Of Weighted Polynomial Approximation by : H N Mhaskar
Download or read book Introduction To The Theory Of Weighted Polynomial Approximation written by H N Mhaskar and published by World Scientific. This book was released on 1997-01-04 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.
Download or read book Polytopes written by Tibor Bisztriczky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject. The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex. With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes. For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.
Book Synopsis Approximation by Polynomials with Integral Coefficients by : Le Baron O. Ferguson
Download or read book Approximation by Polynomials with Integral Coefficients written by Le Baron O. Ferguson and published by American Mathematical Soc.. This book was released on 1980 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses two questions that include: 'What functions can be approximated by polynomials whose coefficients are integers?' and 'How well are they approximated (Jackson type theorems)?'
Book Synopsis Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 by : Walter Edwin Sewell
Download or read book Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 written by Walter Edwin Sewell and published by Princeton University Press. This book was released on 2016-03-02 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9, will be forthcoming.
Book Synopsis Theory of Uniform Approximation of Functions by Polynomials by : Vladislav K. Dzyadyk
Download or read book Theory of Uniform Approximation of Functions by Polynomials written by Vladislav K. Dzyadyk and published by Walter de Gruyter. This book was released on 2008-09-25 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough, self-contained and easily accessible treatment of the theory on the polynomial best approximation of functions with respect to maximum norms. The topics include Chebychev theory, Weierstraß theorems, smoothness of functions, and continuation of functions.
Book Synopsis Polytopes - Combinations and Computation by : Gil Kalai
Download or read book Polytopes - Combinations and Computation written by Gil Kalai and published by Springer Science & Business Media. This book was released on 2000-08-01 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions motivated by the desire to understand the complexity of the simplex algorithm, or the need to study facets for use in cutting plane procedures. In addition, algorithms now provide the means to computationally study polytopes, to compute their parameters such as flag vectors, graphs and volumes, and to construct examples of large complexity. The papers of this volume thus display a wide panorama of connections of polytope theory with other fields. Areas such as discrete and computational geometry, linear and combinatorial optimization, and scientific computing have contributed a combination of questions, ideas, results, algorithms and, finally, computer programs.
Book Synopsis Polynomial Approximation by : Robert P. Feinerman
Download or read book Polynomial Approximation written by Robert P. Feinerman and published by . This book was released on 1973 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem by : David E. Handelman
Download or read book Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem written by David E. Handelman and published by . This book was released on 2014-01-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Limit Theorems of Polynomial Approximation with Exponential Weights by : Michael I. Ganzburg
Download or read book Limit Theorems of Polynomial Approximation with Exponential Weights written by Michael I. Ganzburg and published by American Mathematical Soc.. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.
Book Synopsis Polynomial Approximation by the Method of Least Squares by : Harold Thayer Davis
Download or read book Polynomial Approximation by the Method of Least Squares written by Harold Thayer Davis and published by . This book was released on 1933 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Polynomial Approximation by : David C. Lund
Download or read book Polynomial Approximation written by David C. Lund and published by . This book was released on 1964 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Limit Theorems of Polynomial Approximation with Exponential Weights by : Michael I. Ganzburg
Download or read book Limit Theorems of Polynomial Approximation with Exponential Weights written by Michael I. Ganzburg and published by American Mathematical Society(RI). This book was released on 2014-09-11 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.
Book Synopsis Topics in Hyperplane Arrangements, Polytopes and Box-Splines by : Corrado De Concini
Download or read book Topics in Hyperplane Arrangements, Polytopes and Box-Splines written by Corrado De Concini and published by Springer Science & Business Media. This book was released on 2010-08-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory. This book, written by two distinguished authors, engages a broad audience by proving the a strong foudation. This book may be used in the classroom setting as well as a reference for researchers.
Book Synopsis Topics in Polynomials by : G. V. Milovanovi?
Download or read book Topics in Polynomials written by G. V. Milovanovi? and published by World Scientific. This book was released on 1994 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution.
Book Synopsis Topics in Polynomial and Rational Interpolation and Approximation by : Richard S. Varga
Download or read book Topics in Polynomial and Rational Interpolation and Approximation written by Richard S. Varga and published by . This book was released on 1982 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
