Best Approximation In Normed Linear Spaces By Elements Of Linear Subspaces
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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.
The Theory Of Best Approximation And Functional Analysis
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Author : Ivan Singer
language : en
Publisher: SIAM
Release Date : 1974-06-01
The Theory Of Best Approximation And Functional Analysis written by Ivan Singer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-06-01 with Mathematics categories.
Presents results and problems in the modern theory of best approximation, in which the methods of functional analysis are applied in a consequent manner.
Duality For Nonconvex Approximation And Optimization
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Author : Ivan Singer
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-12
Duality For Nonconvex Approximation And Optimization 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 2007-03-12 with Mathematics categories.
The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.
The Theory Of Best Approximation And Functional Analysis
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Author : Ivan Singer
language : en
Publisher: SIAM
Release Date : 1974-01-01
The Theory Of Best Approximation And Functional Analysis written by Ivan Singer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-01-01 with Mathematics categories.
Results and problems in the modern theory of best approximation, in which the methods of functional analysis are applied in a consequent manner. This modern theory constitutes both a unified foundation for the classical theory of best approximation and a powerful tool for obtaining new results.
Geometric Approximation Theory
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Author : Alexey R. Alimov
language : en
Publisher: Springer Nature
Release Date : 2022-03-29
Geometric Approximation Theory written by Alexey R. Alimov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-29 with Mathematics categories.
This monograph provides a comprehensive introduction to the classical geometric approximation theory, emphasizing important themes related to the theory including uniqueness, stability, and existence of elements of best approximation. It presents a number of fundamental results for both these and related problems, many of which appear for the first time in monograph form. The text also discusses the interrelations between main objects of geometric approximation theory, formulating a number of auxiliary problems for demonstration. Central ideas include the problems of existence and uniqueness of elements of best approximations as well as properties of sets including subspaces of polynomials and splines, classes of rational functions, and abstract subsets of normed linear spaces. The book begins with a brief introduction to geometric approximation theory, progressing through fundamental classical ideas and results as a basis for various approximation sets, suns, and Chebyshev systems. It concludes with a review of approximation by abstract sets and related problems, presenting novel results throughout the section. This text is suitable for both theoretical and applied viewpoints and especially researchers interested in advanced aspects of the field.
Constructive Aspects Of Functional Analysis
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Author : Giuseppe Geymonat
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-21
Constructive Aspects Of Functional Analysis written by Giuseppe Geymonat 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 2011-06-21 with Mathematics categories.
A. Balakrishnan: A constructive approach to optimal control.- R. Glowinski: Méthodes itératives duales pour la minimisation de fonctionnelles convexes.- J.L. Lions: Approximation numérique des inéquations d’évolution.- G. Marchuk: Introduction to the methods of numerical analysis.- U. Mosco: An introduction to the approximate solution of variational inequalities.- I. Singer: Best approximation in normed linear spaces.- G. Strang: A Fourier analysis of the finite element variational method.- M. Zerner: Caractéristiques d’approximation des compacts dans les espaces fonctionnels et problèmes aux limites elliptiques.
Best Approximation By Linear Superpositions Approximate Nomography
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Author : S. I͡A. Khavinson
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-01-01
Best Approximation By Linear Superpositions Approximate Nomography written by S. I͡A. Khavinson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions D considered as a sub-space of the space of continous functions C(X) on a compact space X. Such properties as density of D in C(X), its closedness, proximality, etc. are studied in great detail. The approach to these and other problems based on duality and the Hahn-Banach theorem is emphasized. Also, considerable attention is given to the discussion of the Diliberto-Straus algorithm for finding the best approximation of a given function by linear superpositions.
Linear Approximation
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Author : Arthur Sard
language : en
Publisher: American Mathematical Soc.
Release Date : 1963
Linear Approximation written by Arthur Sard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Mathematics categories.
Many approximations are linear, that is, conform to the principle of super-position, and may profitably be studied by means of the theory of linear spaces. This book sets forth the pertinent parts of that theory, with particular attention to the key spaces $C_n, B, K$, and Hilbert space.
Linear Operators And Approximation Lineare Operatoren Und Approximation
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Author : Bautzer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Linear Operators And Approximation Lineare Operatoren Und Approximation written by Bautzer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
These proceedings contain the lectures presented at the Conference on Linear Operators and Approximation held at the Oberwolfach Mathematical Research In stitute, August 14-22, 1971. There were thirty-eight such lectures while four addi tional papers, subsequently submitted in writing, are also included in this volume. Two of the three lectures presented by Russian mathematicians are rendered in English, the third in Russian. Furthermore, there is areport on new and unsolved problems based upon special problem sessions, with later communications from the participants. In fact, two of the papers inc1uded are devoted to solutions of some of the problems posed. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily somewhat arbitrary. Thus Chapter I on Operator Theory is concerned with linear and non linear semi-groups, structure of single operators, unitary operators, spectral and ergodic theory. Chapter Il on Topics in Functional Analysis inc1udes papers on Riesz spaces, boundedness theorems, generalized limits, and distributions. Chapter III, entitled "Approximation in Abstract Spaces", ranges from characterizations of c1asses of functions in approximation theory to approximation-theoretical topics connected with extensions to Banach (or more general) spaces. Chapter IV contains papers on harmonic analysis in connection with approximation and, finally, Chapter V is devoted to approximation by splines, algebraic polynomials, rational functions, and to Pade approximation. A large part of the general editorial work connected with these proceedings was competently handled by Miss F. Feber, while G.
Numerical Mathematics
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Author : Günther Hämmerlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Mathematics written by Günther Hämmerlin 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.
"In truth, it is not knowledge, but learning, not possessing, but production, not being there, but travelling there, which provides the greatest pleasure. When I have completely understood something, then I turn away and move on into the dark; indeed, so curious is the insatiable man, that when he has completed one house, rather than living in it peacefully, he starts to build another. " Letter from C. F. Gauss to W. Bolyai on Sept. 2, 1808 This textbook adds a book devoted to applied mathematics to the series "Grundwissen Mathematik. " Our goals, like those of the other books in the series, are to explain connections and common viewpoints between various mathematical areas, to emphasize the motivation for studying certain prob lem areas, and to present the historical development of our subject. Our aim in this book is to discuss some of the central problems which arise in applications of mathematics, to develop constructive methods for the numerical solution of these problems, and to study the associated questions of accuracy. In doing so, we also present some theoretical results needed for our development, especially when they involve material which is beyond the scope of the usual beginning courses in calculus and linear algebra. This book is based on lectures given over many years at the Universities of Freiburg, Munich, Berlin and Augsburg.