Greedy Approximation
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Greedy Approximation
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Author : Vladimir Temlyakov
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08
Greedy Approximation written by Vladimir Temlyakov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Computers categories.
This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research.
Banach Spaces And Their Applications In Analysis
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Author : Beata Randrianantoanina
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Banach Spaces And Their Applications In Analysis written by Beata Randrianantoanina and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.
In recent years there has been a surge of profound new developments in various aspects of analysis whose connecting thread is the use of Banach space methods. Indeed, many problems seemingly far from the classical geometry of Banach spaces have been solved using Banach space techniques. This volume contains papers by participants of the conference "Banach Spaces and their Applications in Analysis", held in May 2006 at Miami University in Oxford, Ohio, in honor of Nigel Kalton's 60th birthday. In addition to research articles contributed by participants, the volume includes invited expository articles by principal speakers of the conference, who are leaders in their areas. These articles present overviews of new developments in each of the conference's main areas of emphasis, namely nonlinear theory, isomorphic theory of Banach spaces including connections with combinatorics and set theory, algebraic and homological methods in Banach spaces, approximation theory and algorithms in Banach spaces. This volume also contains an expository article about the deep and broad mathematical work of Nigel Kalton, written by his long time collaborator, Gilles Godefroy. Godefroy's article, and in fact the entire volume, illustrates the power and versatility of applications of Banach space methods and underlying connections between seemingly distant areas of analysis.
Sparse Approximation With Bases
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Author : Vladimir Temlyakov
language : en
Publisher: Birkhäuser
Release Date : 2015-03-27
Sparse Approximation With Bases written by Vladimir Temlyakov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-27 with Mathematics categories.
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and does not require a broad background in the field.
Multivariate Approximation
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Author : V. Temlyakov
language : en
Publisher: Cambridge University Press
Release Date : 2018-07-19
Multivariate Approximation written by V. Temlyakov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-19 with Computers categories.
Self-contained presentation of multivariate approximation from classical linear approximation to contemporary nonlinear approximation.
Model Reduction And Approximation
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Author : Peter Benner
language : en
Publisher: SIAM
Release Date : 2017-07-06
Model Reduction And Approximation written by Peter Benner and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-06 with Science categories.
Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques
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Author : Klaus Jansen
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-08-11
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques written by Klaus Jansen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-11 with Computers categories.
This book constitutes the joint refereed proceedings of the 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2004 and the 8th International Workshop on Randomization and Computation, RANDOM 2004, held in Cambridge, MA, USA in August 2004. The 37 revised full papers presented were carefully reviewed and selected from 87 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, approximation classes, online problems, graph algorithms, cuts, geometric computations, network design and routing, packing and covering, scheduling, game theory, design and analysis of randomised algorithms, randomized complexity theory, pseudorandomness, derandomization, probabilistic proof systems, error-correcting codes, and other applications of approximation and randomness.
Handbook Of Approximation Algorithms And Metaheuristics
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Author : Teofilo F. Gonzalez
language : en
Publisher: CRC Press
Release Date : 2007-05-15
Handbook Of Approximation Algorithms And Metaheuristics written by Teofilo F. Gonzalez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-15 with Computers categories.
Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical applications. It is the first book to comprehensively study both approximation algorithms and metaheuristics. Starting with basic approaches, the handbook presents the methodologies to design and analyze efficient approximation algorithms for a large class of problems, and to establish inapproximability results for another class of problems. It also discusses local search, neural networks, and metaheuristics, as well as multiobjective problems, sensitivity analysis, and stability. After laying this foundation, the book applies the methodologies to classical problems in combinatorial optimization, computational geometry, and graph problems. In addition, it explores large-scale and emerging applications in networks, bioinformatics, VLSI, game theory, and data analysis. Undoubtedly sparking further developments in the field, this handbook provides the essential techniques to apply approximation algorithms and metaheuristics to a wide range of problems in computer science, operations research, computer engineering, and economics. Armed with this information, researchers can design and analyze efficient algorithms to generate near-optimal solutions for a wide range of computational intractable problems.
String Processing And Information Retrieval
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Author : Gabriele Fici
language : en
Publisher: Springer
Release Date : 2017-09-14
String Processing And Information Retrieval written by Gabriele Fici and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-14 with Computers categories.
This book constitutes the proceedings of the 24th International Symposium on String Processing and Information Retrieval, SPIRE 2017, held in Palermo, Italy, in September 2017. The 26 papers presented in this volume were carefully reviewed and selected from 71 submissions. They focus on fundamental studies on string processing and information retrieval, as well as on computational biology.
Foundations Of Computational Mathematics Santander 2005
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Author : Society for the Foundation of Computational Mathematics
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-29
Foundations Of Computational Mathematics Santander 2005 written by Society for the Foundation of Computational Mathematics and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-29 with Mathematics categories.
Surveys and summaries of latest research in numerical analysis, optimization, computer algebra and scientific computing.
Mathematical Foundations Of Computer Science 2005
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Author : Joanna Jedrzejowicz
language : en
Publisher: Springer
Release Date : 2005-09-14
Mathematical Foundations Of Computer Science 2005 written by Joanna Jedrzejowicz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-14 with Computers categories.
This volume contains the papers presented at the 30th Symposium on Mathematical Foundations of Computer Science (MFCS 2005) held in Gdansk, Poland from August 29th to September 2nd, 2005.