Global Smoothness And Shape Preserving Interpolation By Classical Operators

Author : Sorin G. Gal
Publisher : Springer Science & Business Media
Page : 155 pages
File Size : 41,7 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9780817644017

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Global Smoothness and Shape Preserving Interpolation by Classical Operators by Sorin G. Gal Pdf

This monograph examines in detail two aspects in the field of interpolation of functions -the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP). By considering well-known classical interpolation operators such as Lagrange, Grünwald, Hermite-Fejér and Shepard type, the study is mainly developed for the univariate and bivariate cases. One of the first books on the subject, it presents to the reader, recent work featuring many new interesting results in this field, including an excellent survey of past research. Accompanied by numerous open problems, an updated set of references, and an appendix featuring illustrations of nine types of Shepard surfaces, this unique text is best suited to graduate students and researchers in mathematical analysis, interpolation of functions, pure and applied mathematicians in numerical analysis, approximation theory, data fitting, computer aided geometric design, fluid mechanics, and engineering researchers.

Author : Sorin Gal
Publisher : Birkhäuser
Page : 146 pages
File Size : 43,8 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0817670971

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Global Smoothness and Shape Preserving Interpolation by Classical Operators by Sorin Gal Pdf

This monograph examines in detail two aspects in the field of interpolation of functions -the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP). By considering well-known classical interpolation operators such as Lagrange, Grünwald, Hermite-Fejér and Shepard type, the study is mainly developed for the univariate and bivariate cases. One of the first books on the subject, it presents to the reader, recent work featuring many new interesting results in this field, including an excellent survey of past research. Accompanied by numerous open problems, an updated set of references, and an appendix featuring illustrations of nine types of Shepard surfaces, this unique text is best suited to graduate students and researchers in mathematical analysis, interpolation of functions, pure and applied mathematicians in numerical analysis, approximation theory, data fitting, computer aided geometric design, fluid mechanics, and engineering researchers.

Author : Barnabás Bede,Lucian Coroianu,Sorin G. Gal
Publisher : Springer
Page : 458 pages
File Size : 55,7 Mb
Release : 2016-08-08
Category : Mathematics
ISBN : 9783319341897

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Approximation by Max-Product Type Operators by Barnabás Bede,Lucian Coroianu,Sorin G. Gal Pdf

This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly, as bases for the Feller type scheme in terms of the possibilistic integral. These approaches also offer new proofs for the uniform convergence based on a Chebyshev type inequality in the theory of possibility. Researchers in the fields of approximation of functions, signal theory, approximation of fuzzy numbers, image processing, and numerical analysis will find this book most beneficial. This book is also a good reference for graduates and postgraduates taking courses in approximation theory.

Author : Sorin G. Gal
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 43,8 Mb
Release : 2010-06-09
Category : Mathematics
ISBN : 9780817647032

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Shape-Preserving Approximation by Real and Complex Polynomials by Sorin G. Gal Pdf

First comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables Of interest to grad students and researchers in approximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineering Contains many open problems to spur future research Rich and updated bibliography

Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer Nature
Page : 934 pages
File Size : 43,7 Mb
Release : 2022-05-05
Category : Mathematics
ISBN : 9783030841225

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Approximation and Computation in Science and Engineering by Nicholas J. Daras,Themistocles M. Rassias Pdf

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

Author : George A. Anastassiou,Sorin Gal
Publisher : Springer Science & Business Media
Page : 554 pages
File Size : 49,6 Mb
Release : 1999-12-22
Category : Mathematics
ISBN : 0817641513

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Approximation Theory by George A. Anastassiou,Sorin Gal Pdf

We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop erty (GSPP) for almost all known linear approximation operators of ap proximation theory including: trigonometric operators and algebraic in terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.

Author : Anonim
Publisher : Unknown
Page : 784 pages
File Size : 54,9 Mb
Release : 2005
Category : American literature
ISBN : UOM:39015066043251

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American Book Publishing Record by Anonim Pdf

Author : Ram N. Mohapatra,Dipanwita Roy Chowdhury,Debasis Giri
Publisher : Springer
Page : 493 pages
File Size : 47,8 Mb
Release : 2015-06-25
Category : Mathematics
ISBN : 9788132224525

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Mathematics and Computing by Ram N. Mohapatra,Dipanwita Roy Chowdhury,Debasis Giri Pdf

This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. This is the second conference on mathematics and computing organized at Haldia Institute of Technology, India. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computing are of vital importance to a broad range of communities, including mathematicians and computing professionals across different educational levels and disciplines. In current research, modeling and simulation, making decisions under uncertainty and pattern recognition have become very common. Professionals across different educational levels and disciplines need exposure to advances in mathematics and computing. In this context, this book presents research papers on applicable areas of current interest. It also includes papers in which experts summarize research findings, such as signal processing and analysis and low-rank-matrix approximation for solving large systems, which will emerge as powerful tools for further research. These new advances and cutting-edge research in the fields of mathematics and their applications to computing are of paramount importance for young researchers.

Author : Boris I. Kvasov
Publisher : World Scientific
Page : 360 pages
File Size : 53,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9810240104

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Methods of Shape-preserving Spline Approximation by Boris I. Kvasov Pdf

This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces. Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.

Author : Anonim
Publisher : Unknown
Page : 784 pages
File Size : 42,5 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015065183546

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Mathematical Reviews by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 924 pages
File Size : 52,5 Mb
Release : 2006
Category : Mathematics
ISBN : UCBK:C078336162

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Analele Științifice Ale Universității "Al. I. Cuza" Din Iași by Anonim Pdf

Author : Ioannis N. Parasidis,Efthimios Providas,Themistocles M. Rassias
Publisher : Springer Nature
Page : 1050 pages
File Size : 46,8 Mb
Release : 2022-03-10
Category : Mathematics
ISBN : 9783030847210

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Mathematical Analysis in Interdisciplinary Research by Ioannis N. Parasidis,Efthimios Providas,Themistocles M. Rassias Pdf

This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.

Author : Anonim
Publisher : Unknown
Page : 812 pages
File Size : 40,6 Mb
Release : 2003
Category : Dissertations, Academic
ISBN : STANFORD:36105112755660

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Dissertation Abstracts International by Anonim Pdf

Author : Debasis Giri,Ram N. Mohapatra,Heinrich Begehr,Mohammad S. Obaidat
Publisher : Springer
Page : 424 pages
File Size : 51,7 Mb
Release : 2017-04-14
Category : Computers
ISBN : 9789811046421

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Mathematics and Computing by Debasis Giri,Ram N. Mohapatra,Heinrich Begehr,Mohammad S. Obaidat Pdf

This book constitutes the proceedings of the Third International Conference on Mathematics and Computing, ICMC 2017, held in Haldia, India, in January 2017. The 35 papers presented in this volume were carefully reviewed and selected from 129 submissions. They were organized in topical sections named: security and privacy; computing; applied mathematics; and pure mathematics.

Author : Joyce A. Cascio
Publisher : Unknown
Page : 1230 pages
File Size : 52,5 Mb
Release : 2005-05
Category : Electronic
ISBN : 0976237318

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Joyce in the Belly of the Big Truck; Workbook by Joyce A. Cascio Pdf