Algebraic Approximation A Guide To Past And Current Solutions
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Author | : Jorge Bustamante |
Publisher | : Springer Science & Business Media |
Total Pages | : 212 |
Release | : 2011-11-15 |
Genre | : Mathematics |
ISBN | : 3034801947 |
This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.
Author | : Louis Komzsik |
Publisher | : CRC Press |
Total Pages | : 316 |
Release | : 2006-07-20 |
Genre | : Mathematics |
ISBN | : 1420009141 |
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you're looking for approximate solutions to engineering problems, everything y
Author | : Claude Brezinski |
Publisher | : Springer Nature |
Total Pages | : 410 |
Release | : 2020-11-30 |
Genre | : Mathematics |
ISBN | : 3030584186 |
This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.
Author | : Carl De Boor |
Publisher | : American Mathematical Soc. |
Total Pages | : 152 |
Release | : 1986-12-31 |
Genre | : Mathematics |
ISBN | : 9780821867433 |
The papers in this book, first presented at a 1986 AMS Short Course, give a brief introduction to approximation theory and some of its current areas of active research, both theoretical and applied. The first lecture describes and illustrates the basic concerns of the field. Topics highlighted in the other lectures include the following: approximation in the complex domain, $N$-width, optimal recovery, interpolation, algorithms for approximation, and splines, with a strong emphasis on a multivariate setting for the last three topics. The book is aimed at mathematicians interested in an introduction to areas of current research and to engineers and scientists interested in exploring the field for possible applications to their own fields. The book is best understood by those with a standard first graduate course in real and complex analysis, but some of the presentations are accessible with the minimal requirements of advanced calculus and linear algebra.
Author | : Johan De Villiers |
Publisher | : Springer Science & Business Media |
Total Pages | : 418 |
Release | : 2012-06-30 |
Genre | : Mathematics |
ISBN | : 9491216503 |
The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter
Author | : A.A. Gonchar |
Publisher | : Springer Science & Business Media |
Total Pages | : 463 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461229669 |
Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szegö type asymptotics and connections with Jacobi matrices; the convergence theory for Padé and Hermite-Padé approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics.
Author | : Deanne Dickinson |
Publisher | : |
Total Pages | : 118 |
Release | : 1966 |
Genre | : |
ISBN | : |
Author | : George Anastassiou |
Publisher | : CRC Press |
Total Pages | : 626 |
Release | : 2000-09-15 |
Genre | : Mathematics |
ISBN | : 9781584882213 |
Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert. Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers. The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.
Author | : George Anastassiou |
Publisher | : CRC Press |
Total Pages | : 558 |
Release | : 1992-04-24 |
Genre | : Mathematics |
ISBN | : 9780824787080 |
Contains the proceedings of the March 1991 annual conference of the Southeastern Approximation Theorists, in Memphis, Tenn. The 34 papers discuss topics of interest to graduate and professional numerical analysts, applied and industrial mathematicians, engineers, and other scientists such as splines
Author | : J. Ferrera |
Publisher | : Elsevier Science Limited |
Total Pages | : 270 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 9780444518613 |
Inverse problems and approximation in topology. P - The papers are extremely well written and directed to a wide audience, from beginners to experts. An excellent occasion to become engaged with some of the most fruitful mathematics developed during the last decades. It contains a number of seminal contributions by some of the most world leading mathematicians of the second half of the 20th Century. The papers cover a complete range of topics, from the intra-history of the involved mathematics to the very last developments in Differential Equations, Inverse Problems, Analysis, Nonlinear Analysis and Topology. All contributed papers are self-contained works containing rather complete list of references on each of the subjects covered.-