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Author: Vilmos Totik Publisher: American Mathematical Soc. ISBN: 1470416662 Category : Mathematics Languages : en Pages : 112
Book Description
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.
Author: Vilmos Totik Publisher: American Mathematical Soc. ISBN: 1470416662 Category : Mathematics Languages : en Pages : 112
Book Description
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.
Author: David E. Handelman Publisher: Springer ISBN: 3540479511 Category : Mathematics Languages : en Pages : 148
Book Description
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.
Author: Tibor Bisztriczky Publisher: Springer Science & Business Media ISBN: 9401109249 Category : Mathematics Languages : en Pages : 515
Book Description
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.
Author: Sinai Robins Publisher: American Mathematical Society ISBN: 1470470330 Category : Mathematics Languages : en Pages : 352
Book Description
This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class. Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.
Author: Manfred Reimer Publisher: Birkhäuser ISBN: 3034880952 Category : Mathematics Languages : en Pages : 361
Book Description
This book introduces general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book builds the first comprehensive introduction to the theory of generalized hyperinterpolation. Several parts of the book are based on rotation principles, which are presented in the beginning of the book.
Author: Michael I. Ganzburg Publisher: American Mathematical Soc. ISBN: 0821840630 Category : Approximation theory Languages : en Pages : 178
Book Description
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.
Author: Ying Fei Dong Publisher: Springer Science & Business Media ISBN: 3642106307 Category : Computers Languages : en Pages : 1246
Book Description
This book constitutes the refereed proceedings of the 20th International Symposium on Algorithms and Computation, ISAAC 2009, held in Honolulu, Hawaii, USA in December 2009. The 120 revised full papers presented were carefully reviewed and selected from 279 submissions for inclusion in the book. This volume contains topics such as algorithms and data structures, approximation algorithms, combinatorial optimization, computational biology, computational complexity, computational geometry, cryptography, experimental algorithm methodologies, graph drawing and graph algorithms, internet algorithms, online algorithms, parallel and distributed algorithms, quantum computing and randomized algorithms.
Author: Bernd Sturmfels Publisher: American Mathematical Soc. ISBN: 0821804871 Category : Mathematics Languages : en Pages : 162
Book Description
This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Grobner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.
Author: Motoko Kotani Publisher: American Mathematical Soc. ISBN: 0821842692 Category : Number theory Languages : en Pages : 363
Book Description
This volume is an outgrowth of an international conference in honor of Toshikazu Sunada on the occasion of his sixtieth birthday. The conference took place at Nagoya University, Japan, in 2007. Sunada's research covers a wide spectrum of spectral analysis, including interactions among geometry, number theory, dynamical systems, probability theory and mathematical physics. Readers will find papers on trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. This volume also contains an article that presents an overview of Sunada's work in mathematics up to the age of sixty.
Author: Vilmos Totik
Author: Vilmos Totik
Author: David E. Handelman
Author: Tibor Bisztriczky
Author: Z. Ditzian
Author: Sinai Robins
Author: Manfred Reimer
Author: Michael I. Ganzburg
Author: Ying Fei Dong
Author: Bernd Sturmfels
Author: Motoko Kotani