Download or read book Approximation on Subsets of 0 Infinity by Reciprocals of Polynomials written by E. H. Kaufman and published by . This book was released on 1983 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tchebycheff Approximation by Reciprocals of Polynomials on 0 infinity written by Daryl Myron Brink and published by . This book was released on 1972 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation by Polynomials with Integral Coefficients written by Le Baron O. Ferguson and published by American Mathematical Soc.. This book was released on 1980 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses two questions that include: 'What functions can be approximated by polynomials whose coefficients are integers?' and 'How well are they approximated (Jackson type theorems)?'
Download or read book Introduction to the Theory of Weighted Polynomial Approximation written by Hrushikesh Narhar Mhaskar and published by World Scientific. This book was released on 1996 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.
Download or read book Continuity of Best Reciprocal Polynomial Approximation on written by Charles B. Dunham and published by . This book was released on 1979 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuity of the best approximation operator is studied for approximating continuous positive functions tending to zero as x approaches infinity by reciprocals of polynomials on
Download or read book Approximation of Functions by Polynomials and Splines written by S. B. Stechkin and published by American Mathematical Soc.. This book was released on 1981 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers and articles about polynomials and splines pproximation.
Download or read book Sparse Polynomial Approximation of High Dimensional Functions written by Ben Adcock and published by SIAM. This book was released on 2022-02-16 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
Download or read book Recent Trends in Orthogonal Polynomials and Approximation Theory written by Jorge Arvesú and published by American Mathematical Soc.. This book was released on 2010 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo Lopez Lagomasino on his 60th birthday. This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo Lopez Lagomasino.
Download or read book Degree of Approximation by Polynomials in the Complex Domain written by Walter Edwin Sewell and published by . This book was released on 1942 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Weighted Approximation with Varying Weight written by Vilmos Totik and published by Springer. This book was released on 2006-11-15 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Download or read book Approximation with Reciprocals of Polynomials on Compact Sets written by D. J. Leeming and published by . This book was released on 1976 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory best uniform approximation by reciprocals of polynomials on compact sets is developed. In particular an existence theorem is shown to hold in this case. (Author).
Download or read book Approximation Optimization and Mathematical Economics written by Marc Lassonde and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this proceedings volume reflect the current trends in the theory of approximation, optimization and mathematical economics, and include numerous applications. The book will be of interest to researchers and graduate students involved in functional analysis, approximation theory, mathematical programming and optimization, game theory, mathematical finance and economics.
Download or read book On Approximation in the Lp Norm by Reciprocals of Polynomials written by D. Leviatan and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Orthogonal Polynomials written by Gabor Szeg and published by American Mathematical Soc.. This book was released on 1939-12-31 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Extrapolation and Rational Approximation written by Claude Brezinski and published by Springer Nature. This book was released on 2020-11-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1989 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt:
