Approximation With Vector Valued Norms In Linear Spaces PDF Download
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Author | : Alexander Constantine Bacopoulos |
Publisher | : |
Total Pages | : 146 |
Release | : 1966 |
Genre | : Approximation |
ISBN | : |
Download Approximation with Vector-valued Norms in Linear Spaces Book in PDF, ePub and Kindle
Author | : Lee W. Johnson |
Publisher | : |
Total Pages | : 110 |
Release | : 1967 |
Genre | : Functions |
ISBN | : |
Download Approximation of Vector-valued Functions Book in PDF, ePub and Kindle
Author | : João B. Prolla |
Publisher | : North-Holland |
Total Pages | : 219 |
Release | : 1977 |
Genre | : Approximation theory |
ISBN | : 9780444850300 |
Download Approximation of Vector Valued Functions Book in PDF, ePub and Kindle
Author | : Robert Creighton Buck |
Publisher | : |
Total Pages | : 15 |
Release | : 1973 |
Genre | : Functional analysis |
ISBN | : |
Download Approximation Properties of Vector Valued Functions Book in PDF, ePub and Kindle
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 |
Total Pages | : 471 |
Release | : 2013-06-05 |
Genre | : Business & Economics |
ISBN | : 3540248285 |
Download Vector Optimization Book in PDF, ePub and Kindle
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 |
Total Pages | : 240 |
Release | : 1979 |
Genre | : Mathematics |
ISBN | : |
Download Optimization and Approximation Book in PDF, ePub and Kindle
Author | : Frank R. Deutsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468492985 |
Download Best Approximation in Inner Product Spaces Book in PDF, ePub and Kindle
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 |
Total Pages | : 359 |
Release | : 2006-04-18 |
Genre | : Business & Economics |
ISBN | : 0387217436 |
Download Variational Methods in Partially Ordered Spaces Book in PDF, ePub and Kindle
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 |
Total Pages | : 119 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540484043 |
Download Spaces of Approximating Functions with Haar-like Conditions Book in PDF, ePub and Kindle
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 |
Total Pages | : 356 |
Release | : 1981-03-31 |
Genre | : Mathematics |
ISBN | : 9780521295147 |
Download Approximation Theory and Methods Book in PDF, ePub and Kindle
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.