Author: Nikolaĭ Pavlovich KorneĭchukPublisher: Nova Publishers
ISBN: 9781560723615
Category : Mathematics
Languages : en
Pages : 444
Book Description
Extremal Properties of Polynomials & Splines
Extremal Properties of Polynomials and Splines
Author: Nikolaĭ Pavlovich KorneĭchukPublisher: Nova Publishers
ISBN: 9781560723615
Category : Mathematics
Languages : en
Pages : 444
Book Description
Extremal Properties of Polynomials & Splines
Spline Functions and Multivariate Interpolations
Author: Borislav D. BojanovPublisher: Springer
ISBN: 9789401581707
Category : Mathematics
Languages : en
Pages : 278
Book Description
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.
Approximation of Functions by Polynomials and Splines
Author: S. B. StechkinPublisher: American Mathematical Soc.
ISBN: 9780821830499
Category : Mathematics
Languages : en
Pages : 280
Book Description
Papers and articles about polynomials and splines pproximation.
Topics In Polynomials: Extremal Problems, Inequalities, Zeros
Author: Gradimir V MilovanovicPublisher: World Scientific
ISBN: 9814506486
Category : Science
Languages : en
Pages : 844
Book Description
The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution.
Extremal Properties of Polynomials
Author: S. B. StechkinPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 380
Book Description
Proceedings and papers discussing properties of polynomials.
Spline Functions and Multivariate Interpolations
Author: Borislav D. BojanovPublisher: Springer
ISBN: 9780792322290
Category : Computers
Languages : en
Pages : 292
Book Description
This volume provides a comprehensive introduction to the theory of spline functions. Emphasis is given to new developments, such as the general Birkhoff-type interpolation, the extremal properties of splines, their prominent role in the optimal recovery of functions, and multivariate interpolation by polynomials and splines. The book has thirteen chapters dealing, respectively, with interpolation by algebraic polynomials, the space of splines, B-splines, interpolation by spline functions, natural spline functions, perfect splines, monosplines, periodic splines, multivariate B-splines and truncated powers, multivariate spline functions and divided differences, box splines, multivariate mean value interpolation, multivariate polynomial interpolations arising by hyperplanes, and multivariate pointwise interpolation. Some of the results described are presented as exercises and hints are given for their solution. For researchers and graduate students whose work involves approximation theory.
On the Asymptotic Properties of Extremal Polynomials with Prescribed Constant Term
Author: J. L. WalshPublisher:
ISBN:
Category : Extremal problems (Mathematics)
Languages : en
Pages : 32
Book Description
Chebyshev Splines and Kolmogorov Inequalities
Author: Sergey BagdasarovPublisher: Birkhäuser
ISBN: 3034888082
Category : Mathematics
Languages : en
Pages : 213
Book Description
This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity w. In particular, an extensive account is given of structural, limiting, and extremal properties of perfect w-splines generalizing standard polynomial perfect splines in the theory of Sobolev classes. In this context special attention is paid to the qualitative description of Chebyshev w-splines and w-polynomials associated with the Kolmogorov problem of n-widths and sharp additive inequalities between the norms of intermediate derivatives in functional classes with a bounding modulus of continuity. Since, as a rule, the techniques of the theory of Sobolev classes are inapplicable in such classes, novel geometrical methods are developed based on entirely new ideas. The book can be used profitably by pure or applied scientists looking for mathematical approaches to the solution of practical problems for which standard methods do not work. The scope of problems treated in the monograph, ranging from the maximization of integral functionals, characterization of the structure of equimeasurable functions, construction of Chebyshev splines through applications of fixed point theorems to the solution of integral equations related to the classical Euler equation, appeals to mathematicians specializing in approximation theory, functional and convex analysis, optimization, topology, and integral equations .
Exact Constants in Approximation Theory
Author: Nikolaĭ Pavlovich KorneĭchukPublisher: Cambridge University Press
ISBN: 9780521382342
Category : Mathematics
Languages : en
Pages : 472
Book Description
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-widths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists.
Author: Kenneth Ownsworth May