Approximation with Vector-valued Norms in Linear Spaces PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Approximation with Vector-valued Norms in Linear Spaces PDF full book. Access full book title Approximation with Vector-valued Norms in Linear Spaces by Alexander Constantine Bacopoulos. Download full books in PDF and EPUB format.
Author: Alexander Constantine Bacopoulos
Publisher:
ISBN:
Category : Approximation
Languages : en
Pages : 146
Get Book Here
Book Description
Author: Alexander Constantine Bacopoulos
Publisher:
ISBN:
Category : Approximation
Languages : en
Pages : 146
Get Book Here
Book Description
Author: Lee W. Johnson
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 110
Get Book Here
Book Description
Author: Robert Creighton Buck
Publisher:
ISBN:
Category : Functional analysis
Languages : en
Pages : 15
Get Book Here
Book Description
Set theory, Topology, TheoremsWeierstrass theorem, Modules(Mathematics)Let M be a closed C(X) submodule of the space C(X:E) of all bounded continuous functions on the compact space X with values in the normed linear space E. Then, it is shown that the linear functionals phi on C(X:E) that are extreme in the set of those which annihilate M and have norm at most one are exactly those of the form phi(g) = L(g(x sub 0)), where x sub 0 is a point of X and L is an extreme point of the set of functionals of norm one on E that annihilate the subspace M(x sub 0)=(all f(x sub 0) for f epsilon M). The proof uses various forms of the Weierstrass approximation theorem for modules. (Author).
Author: Johannes Jahn
Publisher: Springer Science & Business Media
ISBN: 3540248285
Category : Business & Economics
Languages : en
Pages : 471
Get Book Here
Book Description
In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer ing and economics. Vector optimization problems arise, for exam ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multiobjective pro gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza tion, seems to have important applications to variational inequalities and optimization problems with multivalued data. The roots of vector optimization go back to F. Y. Edgeworth (1881) and V. Pareto (1896) who has already given the definition of the standard optimality concept in multiobjective optimization. But in mathematics this branch of optimization has started with the leg endary paper of H. W. Kuhn and A. W. Tucker (1951). Since about v Vl Preface the end of the 60's research is intensively made in vector optimization.
Author: Werner Krabs
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 240
Get Book Here
Book Description
Author: Frank R. Deutsch
Publisher: Springer Science & Business Media
ISBN: 1468492985
Category : Mathematics
Languages : en
Pages : 344
Get Book Here
Book Description
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.
Author: Alfred Göpfert
Publisher: Springer Science & Business Media
ISBN: 0387217436
Category : Business & Economics
Languages : en
Pages : 359
Get Book Here
Book Description
This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.
Author: Kazuaki Kitahara
Publisher: Springer
ISBN: 3540484043
Category : Mathematics
Languages : en
Pages : 119
Get Book Here
Book Description
Tchebycheff (or Haar) and weak Tchebycheff spaces play a central role when considering problems of best approximation from finite dimensional spaces. The aim of this book is to introduce Haar-like spaces, which are Haar and weak Tchebycheff spaces under special conditions. It studies topics of subclasses of Haar-like spaces, that is, classes of Tchebycheff or weak Tchebycheff spaces, spaces of vector-valued monotone increasing or convex functions and spaces of step functions. The notion of Haar-like spaces provides a general point of view which includes the theories of approximation from the above spaces. The contents are largely new. Graduate students and researchers in approximation theory will be able to read this book with only basic knowledge of analysis, functional analysis and linear algebra.
Author: M. J. D. Powell
Publisher: Cambridge University Press
ISBN: 9780521295147
Category : Mathematics
Languages : en
Pages : 356
Get Book Here
Book Description
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
Author: David G. Luenberger
Publisher: John Wiley & Sons
ISBN: 9780471181170
Category : Technology & Engineering
Languages : en
Pages : 348
Get Book Here
Book Description
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
