Download or read book Trends in Approximation Theory written by Kirill Kopotun and published by . This book was released on 2001 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a carefully edited selection of papers that were presented at the Symposium on Trends in Approximation Theory, held in May 2000, and at the Oslo Conference on Mathematical Methods for Curves and Surfaces, held in July 2000. Mathematical Methods for Curves and Surfaces covers topics from abstract approximation to wavelets.
Download or read book New Trends in Approximation Theory written by Javad Mashreghi and published by Springer. This book was released on 2018-03-28 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.
Download or read book Trends and Applications in Constructive Approximation written by Detlef H. Mache and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics.
Download or read book Exploring Mathematical Analysis Approximation Theory and Optimization written by Nicholas J. Daras and published by Springer Nature. This book was released on 2024-01-04 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.
Download or read book Recent Trends in Orthogonal Polynomials and Approximation Theory written by Jorge Arvesú and published by American Mathematical Soc.. This book was released on 2010 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo Lopez Lagomasino on his 60th birthday. This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo Lopez Lagomasino.
Download or read book New Trends in Shape Modelling and Approximation Methods written by Driss Sbibih and published by Springer. This book was released on 2024-09-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent research results from a selection of the talks presented in the international symposium “New Trends in Approximation and Applications”, held at Oujda, Morocco, in June 2022. The various chapters describe developments in approximation and its different applications including approximation methods in Numerical Analysis, curves and surfaces in CAGD, interpolation and smoothing, shape modelling and computational topology, subdivision schemes and applications, wavelets, and multiresolution methods. The book is addressed to researchers in all of these areas as well as in general mathematical modelling.
Download or read book Approximation and Computation written by Walter Gautschi and published by Springer Science & Business Media. This book was released on 2010-10-20 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines; - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in the computational and applied sciences.
Download or read book Approximation Theory and Approximation Practice Extended Edition written by Lloyd N. Trefethen and published by SIAM. This book was released on 2019-01-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
Download or read book Faster Algorithms Via Approximation Theory written by Sushant Sachdeva and published by . This book was released on 2014-03-28 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Faster Algorithms via Approximation Theory illustrates how classical and modern techniques from approximation theory play a crucial role in obtaining results that are relevant to the emerging theory of fast algorithms. The key lies in the fact that such results imply faster ways to approximate primitives such as products of matrix functions with vectors and, to compute matrix eigenvalues and eigenvectors, which are fundamental to many spectral algorithms. The first half of the book is devoted to the ideas and results from approximation theory that are central, elegant, and may have wider applicability in theoretical computer science. These include not only techniques relating to polynomial approximations but also those relating to approximations by rational functions and beyond. The remaining half illustrates a variety of ways that these results can be used to design fast algorithms. Faster Algorithms via Approximation Theory is self-contained and should be of interest to researchers and students in theoretical computer science, numerical linear algebra, and related areas.
Download or read book Multivariate Approximation written by Werner Haussmann and published by De Gruyter Akademie Forschung. This book was released on 1997 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third edition of the leading practitioner's work on freedom of information. Designed to provide in-depth legal analysis and practical guidance, this book has become the first port of call for anyone either seeking or handling requests for official information. The latest edition maintains its authorship of expert lawyers. The two years since the previous edition have seen numerous important decisions from the courts and from the Information Tribunal on freedom of information law. The learning from all these has been incorporated into the text, enabling a practitioner to see immediately all relevant cases and the principles that emerge from them.The book is logically organised so that the practitioner can quickly find the topic of choice. The work commences with an historical analysis that sets out the object of the legislation and its relationship with other aspects of public law. Full references to Hansard and other Parliamentary materials is provided. This is followed by a summary of the regime in five comparative jurisdictions, providing a useful testbed for anticipated effects of disclosure and a normative yardstick. The impact of the Human Rights Act 1998 is given separate consideration. Next follows a series of chapters dealing with rights of access under provisions apart from the FOI Act: access to information held by EU bodies; access to information under the Data Protection Act; access to information under the Environmental Information Regulations; public records; and access under numerous other provisions in legislation. Together, these provide the practitioner with sources of access that might otherwise be overlooked. All are arranged thematically.The book then considers practical aspects of information requests: the persons who may make them; the bodies to whom they may be made; the time allowed for responding; the modes of response; fees and vexatious requests; the duty to advise and assist; the codes of practice; government guidance and its status; transferring of requests; third party consultation.The next 13 chapters, comprising over half the book, are devoted to exemptions. These start with two important chapters dealing with general principles, including the notions of "prejudice" and the "public interest." The arrangement of these chapters reflects the arrangement of the FOI Act, but the text is careful to include analogous references to the Environmental Information Regulations and the Data Protection Act 1998. With each chapter, the exemption is carefully analysed, starting with its Parliamentary history (giving full references to Hansard and other Parliamentary material) and the treatment given in the comparative jurisdictions. The analysis then turns to consider all court judgments and tribunal decisions dealing with the exemption. The principles are stated in the text, with footnotes giving all available references. Whether to prepare a case or to prepare a response to a request, these chapters allow the practitioner to get on top of the exemption rapidly and authoritatively.The book concludes with three chapters setting out the role of the Information Commissioner and the Tribunal, appeals and enforcement. The chapter on appeals allows the practitioner to be familiar with the processes followed in the tribunal, picking up on the jurisprudence as it has emerged over the last five or so years.Appendices include: precedent requests for information; a step-by-step guide to responding to a request; comparative tables; and a table of the FOI Act's Parliamentary history. Finally, the book includes an annotated copy of the FOIA Act, the Data Protection Act 1998, the Environmental Information Regulations 2004, all subordinate legislation made under them, EU legislation, Tribunal rules and practice directions, and the Codes of Practice.Throughout the book, full web references are given (including to all cases), facilitating ready access to primary material.From the reviews of previous editions:"The depth of analysis and thought that Philip Coppel brings to the topic is evident throughout....Careful analysis is a hallmark of the book which reflects, not merely an academic interest in the legal regime but a real and active interest in the wider societal issues involved in the development of the law in this area.... The text delivers excellent value for anyone working seriously in this area." - Rosemary Jay in Freedom of Information Journal"Encyclopaedic and authoritative...a very useful guide to practitioners as well as those seeking official information" - New Law Journal"This is not just a book for the library it is also a book to be held close at hand on any practitioner's desk, or in any public authority boardroom - the hope expressed by Coppel that his book will assist in resolving [FOI Act] complexities and in revealing its subtleties is realised in a well composed and intelligently written volume." - Solicitors Journal"...The best single resource in this area of the law.... Any practitioner who needs to consider information rights owes a considerable debt of thanks to Philip Coppel and his fellow authors." - Jonathan Crow QC in Public Law"This is an outstanding piece of legal scholarship, which will provide invaluable assistance to practitioners interested in information rights whether they be based in the United Kingdom or in comparable overseas jurisdictions." - John Griffiths SC in Australian Journal of Administrative Law
Download or read book Approximation Theory and Related Applications written by Yurii Kharkevych and published by Mdpi AG. This book was released on 2023-01-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world's leading scientists presented in this book reflect new trends in approximation theory and related topics.
Download or read book Exploring Mathematical Analysis Approximation Theory and Optimization written by Nicholas J. Daras and published by Springer. This book was released on 2023-12-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.
Download or read book Approximation Theory written by Luc Wuytack and published by North-Holland. This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: /homepage/sac/cam/na2000/index.htmllt;/HREF> 7-Volume Set now available at special set price ! The field of numerical analysis has witnessed many significant developments in the 20th century and will continue to enjoy major new advances in the years ahead. Therefore, it seems appropriate to compile a "state-of-the-art" volume devoted to numerical analysis in the 20th century. This volume on "Approximation Theory" is the first of seven volumes that will be published in this Journal. It brings together the papers dealing with historical developments, survey papers and papers on recent trends in selected areas. In his paper, G.A. Watson gives an historical survey of methods for solving approximation problems in normed linear spaces. He considers approximation in Lp and Chebyshev norms of real functions and data. Y. Nievergelt describes the history of least-squares approximation. His paper surveys the development and applications of ordinary, constrained, weighted and total least-squares approximation. D. Leviatan discusses the degree of approximation of a function in the uniform of Lp norm. The development of numerical algorithms is strongly related to the type of approximating functions that are used, e.g. orthogonal polynomials, splines and wavelets, and several authors describe these different approaches. E. Godoy, A. Ronveaux, A. Zarzo, and I. Area treat the topic of classical orthogonal polynomials R. Piessens, in his paper, illustrates the use of Chebyshev polynomials in computing integral transforms and for solving integral equations. Some developments in the use of splines are described by G. Nurnberger, F. Zeilfelder (for the bivariate case), and by R.-H. Wang in the multivariate case. For the numercial treatment of functions of several variables, radial basis functions are useful tools. R. Schaback treats this topic in his paper. Certain aspects of the computation of Daubechie wavelets are explained and illustrated in the paper by C. Taswell, P. Guillaume and A. Huard explore the case of multivariate Padee approximation. Special functions have played a crucial role in approximating the solutions of certain scientific problems. N. Temme illustrates the usefulness of parabolic cylinder functions and J.M. Borwein, D.M. Bradley, R.E. Crandall provide a compendium of evaluation methods for the Riemann zeta function. S. Lewanowicz develops recursion formulae for basic hypergeometric functions. Aspects of the spectral theory for the classical Hermite differential equation appear in the paper by W.M. Everitt, L.L. Littlejohn and R. Wellman. Many applications of approximation theory are to be found in linear system theory and model reduction. The paper of B. De Schutter gives an overview of minimal state space realization in linear system theory and the paper by A. Bultheel and B. De Moor describes the use of rational approximation in linear systems and control. For problems whose solutions may have singularities or infinite domains, sinc approximation methods are of value. F. Stenger summarizes the results in this field in his contribution. G. Alefeld and G. Mayer provide a survey of the historical developoment of interval analysis, including several applications of interval mathematics to numerical computing. These papers illustrate the profound impact that ideas of approximation theory have had in the creation of numerical algorithms for solving real-world scientific problems. Furthermore, approximation-theortical concepts have proved to be basic tools in the analysis of the applicability of these algorithms. We thank the authors of the above papers for their willingness to contribute to this volume. Also, we very much appreciate the referees for their role in making this volume a valuable source of information for
Download or read book Faster Algorithms Via Approximation Theory written by Sushant Sachdeva and published by . This book was released on 2014 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents ideas and techniques from approximation theory for approximating functions such as xs; x-1 and e-x, and demonstrates how these results play a crucial role in the design of fast algorithms for problems which are increasingly relevant. The key lies in the fact that such results imply faster ways to compute primitives such as Asv, A-1v, exp(-A)v, Eigenvalues, and Eigenvectors, which are fundamental to many spectral algorithms. Indeed, many fast algorithms reduce to the computation of such primitives, which have proved useful for speeding up several fundamental computations such as random walk simulation, graph partitioning, and solving systems of linear equations.
Download or read book Approximation Algorithms for Complex Systems written by Emmanuil H Georgoulis and published by Springer Science & Business Media. This book was released on 2011-01-04 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects up-to-date papers from world experts in a broad variety of relevant applications of approximation theory, including dynamical systems, multiscale modelling of fluid flow, metrology, and geometric modelling to mention a few. The 14 papers in this volume document modern trends in approximation through recent theoretical developments, important computational aspects and multidisciplinary applications. The book is arranged in seven invited surveys, followed by seven contributed research papers. The surveys of the first seven chapters are addressing the following relevant topics: emergent behaviour in large electrical networks, algorithms for multivariate piecewise constant approximation, anisotropic triangulation methods in adaptive image approximation, form assessment in coordinate metrology, discontinuous Galerkin methods for linear problems, a numerical analyst's view of the lattice Boltzmann method, approximation of probability measures on manifolds. Moreover, the diverse contributed papers of the remaining seven chapters reflect recent developments in approximation theory, approximation practice and their applications. Graduate students who wish to discover the state of the art in a number of important directions of approximation algorithms will find this a valuable volume. Established researchers from statisticians through to fluid modellers will find interesting new approaches to solving familiar but challenging problems. This book grew out of the sixth in the conference series on "Algorithms for Approximation", which took place from 31st August to September 4th 2009 in Ambleside in the Lake District of the United Kingdom.
Download or read book Nonlinear Analysis written by Qamrul Hasan Ansari and published by Springer. This book was released on 2014-06-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Download or read book A Geometry of Approximation written by Piero Pagliani and published by Springer Science & Business Media. This book was released on 2008-10-09 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost. Such an approach endows the present treatise with a unique character. Due to this uniqueness in the treatment of the subject, the book will be useful to researchers, graduate and pre-graduate students from various disciplines, such as computer science, mathematics and philosophy. It features an impressive number of examples supported by about 40 tables and 230 figures. The comprehensive index of concepts turns the book into a sort of encyclopaedia for researchers from a number of fields. 'A Geometry of Approximation' links many areas of academic pursuit without losing track of its focal point, Rough Sets.
