Interpolation Processes

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Publisher : Springer Science & Business Media
ISBN 13 : 3540683496
Total Pages : 452 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Interpolation Processes by : Giuseppe Mastroianni

Download or read book Interpolation Processes written by Giuseppe Mastroianni and published by Springer Science & Business Media. This book was released on 2008-08-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that - peared in the last fty years, but a few of them are devoted only to interpolation processes. An example is the book of J. Szabados and P. Vértesi: Interpolation of Functions, published in 1990 by World Scienti c. Also, two books deal with a special interpolation problem, the so-called Birkhoff interpolation, written by G.G. Lorentz, K. Jetter, S.D. Riemenschneider (1983) and Y.G. Shi (2003). The classical books on interpolation address numerous negative results, i.e., - sultsondivergentinterpolationprocesses,usuallyconstructedoversomeequidistant system of nodes. The present book deals mainly with new results on convergent - terpolation processes in uniform norm, for algebraic and trigonometric polynomials, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. Basic tools in this eld (orthogonal polynomials, moduli of smoothness,K-functionals, etc.), as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. The rstchapterprovidesanaccountofbasicfactsonapproximationbyalgebraic and trigonometric polynomials introducing the most important concepts on appro- mation of functions. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant.

Interpolation Theory and Applications

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821842072
Total Pages : 370 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Interpolation Theory and Applications by : Michael Cwikel

Download or read book Interpolation Theory and Applications written by Michael Cwikel and published by American Mathematical Soc.. This book was released on 2007 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). The central topic of this book is interpolation theory in its broadest sense, with special attention to its applications to analysis. The articles include applications to classical analysis, harmonic analysis, partial differential equations, function spaces, image processing, geometry of Banach spaces, and more. This volume emphasizes remarkable connections between several branches of pure and applied analysis. Graduate students and researchers in analysis will find it very useful.

Interpolation Theory

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Publisher : Edizioni della Normale
ISBN 13 : 9788876426391
Total Pages : 199 pages
Book Rating : 4.4/5 (263 download)

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Book Synopsis Interpolation Theory by : Alessandra Lunardi

Download or read book Interpolation Theory written by Alessandra Lunardi and published by Edizioni della Normale. This book was released on 2018-04-17 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.

Interpolation Spaces

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Publisher : Springer Science & Business Media
ISBN 13 : 3642664512
Total Pages : 218 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Interpolation Spaces by : J. Bergh

Download or read book Interpolation Spaces written by J. Bergh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boe1 Engebrand, Lena Mattsson and Birgit Hoglund for their expert typing of our manuscript.

Birkhoff Interpolation

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Publisher : Cambridge University Press
ISBN 13 : 9780521302395
Total Pages : 308 pages
Book Rating : 4.3/5 (23 download)

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Book Synopsis Birkhoff Interpolation by : G. G. Lorentz

Download or read book Birkhoff Interpolation written by G. G. Lorentz and published by Cambridge University Press. This book was released on 1984-12-28 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and interpolation in the last twenty years. It presents all the basic material known at the present time in a unified manner. Topics discussed include; applications of Birkhoff interpolation to approximation theory, quadrature formulas and Chebyshev systems; lacunary interpolation at special knots and an introduction to the theory of Birkhoff interpolation by splines.

Interpolation and Approximation

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Publisher : Courier Corporation
ISBN 13 : 0486624951
Total Pages : 418 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Interpolation and Approximation by : Philip J. Davis

Download or read book Interpolation and Approximation written by Philip J. Davis and published by Courier Corporation. This book was released on 1975-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.

The Theory of Splines and Their Applications

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Publisher : Elsevier
ISBN 13 : 1483222950
Total Pages : 297 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis The Theory of Splines and Their Applications by : J. H. Ahlberg

Download or read book The Theory of Splines and Their Applications written by J. H. Ahlberg and published by Elsevier. This book was released on 2016-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.

Introduction to Shannon Sampling and Interpolation Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1461397081
Total Pages : 336 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Introduction to Shannon Sampling and Interpolation Theory by : Robert J. II Marks

Download or read book Introduction to Shannon Sampling and Interpolation Theory written by Robert J. II Marks and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much of that which is ordinal is modeled as analog. Most computational engines on the other hand are dig- ital. Transforming from analog to digital is straightforward: we simply sample. Regaining the original signal from these samples or assessing the information lost in the sampling process are the fundamental questions addressed by sampling and interpolation theory. This book deals with understanding, generalizing, and extending the cardinal series of Shannon sampling theory. The fundamental form of this series states, remarkably, that a bandlimited signal is uniquely specified by its sufficiently close equally spaced samples. The contents of this book evolved from a set of lecture notes prepared for a graduate survey course on Shannon sampling and interpolation theory. The course was taught at the Department of Electrical Engineering at the University of Washington, Seattle. Each of the seven chapters in this book includes a list of references specific to that chapter. A sequel to this book will contain an extensive bibliography on the subject. The author has also opted to include solutions to selected exercises in the Appendix.

Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications

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Publisher : Martino Fine Books
ISBN 13 : 9781614275176
Total Pages : 174 pages
Book Rating : 4.2/5 (751 download)

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Book Synopsis Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications by : Norbert Wiener

Download or read book Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications written by Norbert Wiener and published by Martino Fine Books. This book was released on 2013-11 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2013 Reprint of 1949 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This is the second book by Norbert Wiener on time series and communication engineering. While the first one, "Cybernetics," treated the subject from a general standpoint and was more philosophical than mathematical, the present volume is more technical than theoretical, and forms a kind of companion piece to the first. It is intended as a tool for engineers working in the field of electrical communication and related subjects. The book consists of an introduction, five chapters, and three appendices. After explaining the general outline of the problem in the introduction, the author gives in Chapter I a review of generalized harmonic analysis which is necessary for the understanding of the following chapters. Chapters II and III are devoted to the problems of prediction and filtering respectively. In Chapter IV there is given a brief account of the theory of multiple prediction, that is, the theory of prediction when we deal with more than one time series at the same time. Finally, in Chapter V there is given a short discussion on the application of similar methods to a problem of approximate differentiation.

Spline Functions and Multivariate Interpolations

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Publisher : Springer Science & Business Media
ISBN 13 : 940158169X
Total Pages : 287 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Spline Functions and Multivariate Interpolations by : Borislav D. Bojanov

Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.

Interpolation and Approximation by Polynomials

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Publisher : Springer Science & Business Media
ISBN 13 : 0387216820
Total Pages : 325 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Interpolation and Approximation by Polynomials by : George M. Phillips

Download or read book Interpolation and Approximation by Polynomials written by George M. Phillips and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Theory and Applications of Numerical Analysis

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Publisher : Elsevier
ISBN 13 : 0080519121
Total Pages : 461 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Theory and Applications of Numerical Analysis by : G. M. Phillips

Download or read book Theory and Applications of Numerical Analysis written by G. M. Phillips and published by Elsevier. This book was released on 1996-07-05 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included. - a unique blend of theory and applications - two brand new chapters on eigenvalues and splines - inclusion of formal algorithms - numerous fully worked examples - a large number of problems, many with solutions

The Diversity and Beauty of Applied Operator Theory

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Publisher : Springer
ISBN 13 : 3319759965
Total Pages : 506 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis The Diversity and Beauty of Applied Operator Theory by : Albrecht Böttcher

Download or read book The Diversity and Beauty of Applied Operator Theory written by Albrecht Böttcher and published by Springer. This book was released on 2018-04-27 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 29 invited articles written by participants of the International Workshop on Operator Theory and its Applications held in Chemnitz in 2017. The contributions include both expository essays and original research papers illustrating the diversity and beauty of insights gained by applying operator theory to concrete problems. The topics range from control theory, frame theory, Toeplitz and singular integral operators, Schrödinger, Dirac, and Kortweg-de Vries operators, Fourier integral operator zeta-functions, C*-algebras and Hilbert C*-modules to questions from harmonic analysis, Monte Carlo integration, Fibonacci Hamiltonians, and many more. The book offers researchers in operator theory open problems from applications that might stimulate their work and shows those from various applied fields, such as physics, engineering, or numerical mathematics how to use the potential of operator theory to tackle interesting practical problems.

Interpolation Theory and Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821857748
Total Pages : 374 pages
Book Rating : 4.8/5 (577 download)

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Book Synopsis Interpolation Theory and Applications by : Michael Cwikel

Download or read book Interpolation Theory and Applications written by Michael Cwikel and published by American Mathematical Soc.. This book was released on 2007 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). The central topic of this book is interpolation theory in its broadest sense, with special attention to its applications to analysis. The articles include applications to classical analysis, harmonic analysis, partial differential equations, function spaces, image processing, geometry of Banach spaces, and more. This volume emphasizes remarkable connections between several branches of pure and applied analysis. Graduate students and researchers in analysis will find it very useful.

Improved Signal and Image Interpolation in Biomedical Applications: The Case of Magnetic Resonance Imaging (MRI)

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Author :
Publisher : IGI Global
ISBN 13 : 1605662038
Total Pages : 640 pages
Book Rating : 4.6/5 (56 download)

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Book Synopsis Improved Signal and Image Interpolation in Biomedical Applications: The Case of Magnetic Resonance Imaging (MRI) by : Ciulla, Carlo

Download or read book Improved Signal and Image Interpolation in Biomedical Applications: The Case of Magnetic Resonance Imaging (MRI) written by Ciulla, Carlo and published by IGI Global. This book was released on 2009-03-31 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents novel concepts supported through mathematics to create unique theories related to interpolation"--Provided by publisher.

Operator Algebras, Operator Theory and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 3034601743
Total Pages : 301 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Operator Algebras, Operator Theory and Applications by : J. J. Grobler

Download or read book Operator Algebras, Operator Theory and Applications written by J. J. Grobler and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the eighteenth International Workshop on Operator Theory and Applications (IWOTA), hosted by the Unit for Business Mathematics and Informatics of North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference (as well as these proceedings) was dedicated to Professors Joseph A. Ball and Marinus M. Kaashoek on the occasion of their 60th and 70th birthdays, respectively. This conference had a particular focus on Von Neumann algebras at the interface of operator theory with functional analysis and on applications of operator theory to differential equations.

Noncommutative Function-Theoretic Operator Theory and Applications

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Publisher : Cambridge University Press
ISBN 13 : 131651899X
Total Pages : 439 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Noncommutative Function-Theoretic Operator Theory and Applications by : Joseph A. Ball

Download or read book Noncommutative Function-Theoretic Operator Theory and Applications written by Joseph A. Ball and published by Cambridge University Press. This book was released on 2021-12-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.