Best Approximation In Inner Product Spaces
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Best Approximation In Inner Product Spaces
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Author : Frank R. Deutsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Best Approximation In Inner Product Spaces written by Frank R. Deutsch 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 2012-12-06 with Mathematics categories.
This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book is some knowledge of advanced calculus and linear algebra.
Best Approximation In Inner Product Spaces
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Author : Deutsch
language : en
Publisher:
Release Date : 1998-12-01
Best Approximation In Inner Product Spaces written by Deutsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-01 with categories.
Characterizations Of Inner Product Spaces
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Author : Amir
language : en
Publisher: Birkhäuser
Release Date : 2013-11-21
Characterizations Of Inner Product Spaces written by Amir and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Science categories.
Every mathematician working in Banaeh spaee geometry or Approximation theory knows, from his own experienee, that most "natural" geometrie properties may faH to hold in a generalnormed spaee unless the spaee is an inner produet spaee. To reeall the weIl known definitions, this means IIx 11 = *, where is an inner (or: scalar) product on E, Le. a function from ExE to the underlying (real or eomplex) field satisfying: (i) O for x o. (ii) is linear in x. (iii) = (intherealease, thisisjust =
Approximation Theory In Tensor Product Spaces
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Author : William A. Light
language : en
Publisher: Springer
Release Date : 2006-11-14
Approximation Theory In Tensor Product Spaces written by William A. Light and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Inner Product Spaces And Applications
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Author : T M Rassias
language : en
Publisher: CRC Press
Release Date : 1997-10-08
Inner Product Spaces And Applications written by T M Rassias and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-08 with Mathematics categories.
In this volume, the contributing authors deal primarily with the interaction among problems of analysis and geometry in the context of inner product spaces. They present new and old characterizations of inner product spaces among normed linear spaces and the use of such spaces in various research problems of pure and applied mathematics. The methods employed are accessible to students familiar with normed linear spaces. Some of the theorems presented are at the same time simple and challenging.
Theoretical Numerical Analysis
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Author : Kendall Atkinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-07
Theoretical Numerical Analysis written by Kendall Atkinson 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 2007-06-07 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.
Best Approximation In Normed Linear Spaces By Elements Of Linear Subspaces
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Author : Ivan Singer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-14
Best Approximation In Normed Linear Spaces By Elements Of Linear Subspaces written by Ivan Singer 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 2013-12-14 with Mathematics categories.
A Course On Optimization And Best Approximation
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Author : R. B. Holmes
language : en
Publisher: Springer
Release Date : 2006-11-15
A Course On Optimization And Best Approximation written by R. B. Holmes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Theory Of 2 Inner Product Spaces
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Author : Yeol Je Cho
language : en
Publisher: Nova Publishers
Release Date : 2001
Theory Of 2 Inner Product Spaces written by Yeol Je Cho and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The purpose of this book is to give systematic and comprehensive presentation of theory of n-metric spaces, linear n-normed spaces and n-inner product spaces (and so 2-metric spaces, linear 2-normed spaces and 2-linner product spaces n=2). Since 1963 and 1965, S. Gahler published two papers entitled "2-metrische Raume und ihr topologische Strukhur" and "Lineare 2-normierte Raume", a number of authors have done considerable works on geometric structures of 2-metric spaces and linear 2-normed spaces, and have applied these spaces to several fields of mathematics in many ways. In 1969, S. Gahler introduced also the concept of n metric spaces in a series of his papers entitled "Untersuchungen uber verallemeinerte n-metriscke Raume 1, II, III", which extend the concept of 2-metric spaces to the general case, and provided many properties of topological and geometrical structures. Recently, A. Misiak introduced the concept of n-inner product spaces and extended many results in 2 inner product spaces,which in turn were introduced and studied by C. Diminnie, S. Gahler and A. White, to n-inner product spaces in his doctoral dissertation. This book contains, in short, the latest results on 2-metric spaces and linear 2-normed spaces, 2-inner product spaces, G-inner product spaces, strict convexity and uniform convexity, orthogonal relations, quadratic sets on modules and n-inner product spaces. It is hoped that this book will be devoted to a stimulation of interest in further exploration and to the possible applications in various other branches of mathematics.
The Best Approximation Method An Introduction
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Author : Theodore V. II Hromadka
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Best Approximation Method An Introduction written by Theodore V. II Hromadka 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 2012-12-06 with Technology & Engineering categories.
The most commonly used numerical techniques in solving engineering and mathematical models are the Finite Element, Finite Difference, and Boundary Element Methods. As computer capabilities continue to impro':e in speed, memory size and access speed, and lower costs, the use of more accurate but computationally expensive numerical techniques will become attractive to the practicing engineer. This book presents an introduction to a new approximation method based on a generalized Fourier series expansion of a linear operator equation. Because many engineering problems such as the multi dimensional Laplace and Poisson equations, the diffusion equation, and many integral equations are linear operator equations, this new approximation technique will be of interest to practicing engineers. Because a generalized Fourier series is used to develop the approxi mator, a "best approximation" is achieved in the "least-squares" sense; hence the name, the Best Approximation Method. This book guides the reader through several mathematics topics which are pertinent to the development of the theory employed by the Best Approximation Method. Working spaces such as metric spaces and Banach spaces are explained in readable terms. Integration theory in the Lebesque sense is covered carefully. Because the generalized Fourier series utilizes Lebesque integration concepts, the integra tion theory is covered through the topic of converging sequences of functions with respect to measure, in the mean (Lp), almost uniformly IV and almost everywhere. Generalized Fourier theory and linear operator theory are treated in Chapters 3 and 4.