Constructive Approximation

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Lectures on Constructive Approximation

Author : Volker Michel
Publisher : Springer Science & Business Media
ISBN 13 : 0817684034
Total Pages : 336 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Lectures on Constructive Approximation by : Volker Michel

Download or read book Lectures on Constructive Approximation written by Volker Michel and published by Springer Science & Business Media. This book was released on 2012-12-12 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

Trends and Applications in Constructive Approximation

Author : Detlef H. Mache
Publisher : Springer Science & Business Media
ISBN 13 : 3764373563
Total Pages : 300 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Trends and Applications in Constructive Approximation by : Detlef H. Mache

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.

Constructive Approximation

Author : Michael F. Barnsley
Publisher : Springer
ISBN 13 : 1489968865
Total Pages : 172 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Constructive Approximation by : Michael F. Barnsley

Download or read book Constructive Approximation written by Michael F. Barnsley and published by Springer. This book was released on 2013-12-14 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Constructive Approximation

Author : Ronald A. DeVore
Publisher : Springer Science & Business Media
ISBN 13 : 9783540506270
Total Pages : 468 pages
Book Rating : 4.5/5 (62 download)

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Book Synopsis Constructive Approximation by : Ronald A. DeVore

Download or read book Constructive Approximation written by Ronald A. DeVore and published by Springer Science & Business Media. This book was released on 1993-11-04 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators. Other topics include Weierstrauss and best approximation theorems, properties of polynomials and splines. It contains history and proofs with an emphasis on principal results.

Advanced Problems in Constructive Approximation

Author : Martin D. Buhmann
Publisher : Birkhäuser
ISBN 13 : 3034876009
Total Pages : 286 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Advanced Problems in Constructive Approximation by : Martin D. Buhmann

Download or read book Advanced Problems in Constructive Approximation written by Martin D. Buhmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current form of modern approximation theory is shaped by many new de velopments which are the subject of this series of conferences. The International Meetings on Approximation Theory attempt to keep track in particular of fun damental advances in the theory of function approximation, for example by (or thogonal) polynomials, (weighted) interpolation, multivariate quasi-interpolation, splines, radial basis functions and several others. This includes both approxima tion order and error estimates, as well as constructions of function systems for approximation of functions on Euclidean spaces and spheres. It is a piece of very good fortune that at all of the IDoMAT meetings, col leagues and friends from all over Europe, and indeed some count ries outside Europe and as far away as China, New Zealand, South Africa and U.S.A. came and dis cussed mathematics at IDoMAT conference facility in Witten-Bommerholz. The conference was, as always, held in a friendly and congenial atmosphere. After each meeting, the delegat es were invited to contribute to the proceed ing's volume, the previous one being published in the same Birkhäuser series as this one. The editors were pleased about the quality of the contributions which could be solicited for the book. They are refereed and we should mention our gratitude to the referees and their work.

Recent Advances in Constructive Approximation Theory

Author : Vijay Gupta
Publisher : Springer
ISBN 13 : 3319921657
Total Pages : 295 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Recent Advances in Constructive Approximation Theory by : Vijay Gupta

Download or read book Recent Advances in Constructive Approximation Theory written by Vijay Gupta and published by Springer. This book was released on 2018-07-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.

Constructive Approximation

Author : George G. Lorentz
Publisher : Springer
ISBN 13 : 9783642646102
Total Pages : 0 pages
Book Rating : 4.6/5 (461 download)

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Book Synopsis Constructive Approximation by : George G. Lorentz

Download or read book Constructive Approximation written by George G. Lorentz and published by Springer. This book was released on 2011-12-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last 30 years, Approximation Theory has undergone wonderful develop ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

Constructive Approximation

Author : George G. Lorentz
Publisher : Springer
ISBN 13 :
Total Pages : 674 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Constructive Approximation by : George G. Lorentz

Download or read book Constructive Approximation written by George G. Lorentz and published by Springer. This book was released on 1996-05-14 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last 30 years, Approximation Theory has undergone wonderful develop ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

Continued Fractions: From Analytic Number Theory to Constructive Approximation

Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
ISBN 13 : 0821812009
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Continued Fractions: From Analytic Number Theory to Constructive Approximation by : Bruce C. Berndt

Download or read book Continued Fractions: From Analytic Number Theory to Constructive Approximation written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 1999 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields-from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Padé approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.

Constructive Approximation

Author : George G. Lorentz
Publisher : Springer
ISBN 13 : 9783642609329
Total Pages : 649 pages
Book Rating : 4.6/5 (93 download)

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Book Synopsis Constructive Approximation by : George G. Lorentz

Download or read book Constructive Approximation written by George G. Lorentz and published by Springer. This book was released on 1996 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last 30 years, Approximation Theory has undergone wonderful develop ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

Advances in Constructive Approximation

Author : Marian Neamtu
Publisher :
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Advances in Constructive Approximation by : Marian Neamtu

Download or read book Advances in Constructive Approximation written by Marian Neamtu and published by . This book was released on 2004 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Advances in Constructive Approximation Theory

Author : Vijay Gupta
Publisher : Springer
ISBN 13 : 9783319921648
Total Pages : 291 pages
Book Rating : 4.9/5 (216 download)

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Book Synopsis Recent Advances in Constructive Approximation Theory by : Vijay Gupta

Download or read book Recent Advances in Constructive Approximation Theory written by Vijay Gupta and published by Springer. This book was released on 2018-08-10 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.

Constructive Approximation on the Sphere with Applications to Geomathematics

Author : W. Freeden
Publisher :
ISBN 13 :
Total Pages : 458 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Constructive Approximation on the Sphere with Applications to Geomathematics by : W. Freeden

Download or read book Constructive Approximation on the Sphere with Applications to Geomathematics written by W. Freeden and published by . This book was released on 1998 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geomathematics offers an useful means of assimilating and assessing the ever increasing flow of data from geoscientific and satellite sources, as well as an objective basis for the interpretation, classification, and solution of problems. This volume provides the necessary foundation in sphere oriented mathematics for graduate students and researchers interested in any of the diverse topics of constructive approximation in this area. Aspects of approximation by spherical harmonics, such as spherical splines and wavelets, are discussed in detail, and methods for handling different types of data, such as scalar, vectorial, and tensorial, are each considered in turn. This book presents the most up-to-date structures and methods for the efficient handling of sophisticated measurements and observations, thus reducing time and costs.

Approximation Theory and Approximation Practice, Extended Edition

Author : Lloyd N. Trefethen
Publisher : SIAM
ISBN 13 : 1611975948
Total Pages : 375 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Approximation Theory and Approximation Practice, Extended Edition by : Lloyd N. Trefethen

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.

Greedy Approximation

Author : Vladimir Temlyakov
Publisher : Cambridge University Press
ISBN 13 : 1139502808
Total Pages : 433 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Greedy Approximation by : Vladimir Temlyakov

Download or read book Greedy Approximation written by Vladimir Temlyakov and published by Cambridge University Press. This book was released on 2011-09-08 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exact Constants in Approximation Theory

Author : Nikolaĭ Pavlovich Korneĭchuk
Publisher : Cambridge University Press
ISBN 13 : 9780521382342
Total Pages : 472 pages
Book Rating : 4.3/5 (823 download)

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Book Synopsis Exact Constants in Approximation Theory by : Nikolaĭ Pavlovich Korneĭchuk

Download or read book Exact Constants in Approximation Theory written by Nikolaĭ Pavlovich Korneĭchuk and published by Cambridge University Press. This book was released on 1991-06-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-widths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists.

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1490110127
Total Pages : 1001 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition by :

Download or read book Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1001 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Approximation Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Approximation Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.