Download or read book Smoothing and Approximation of Functions written by Harold S. Shapiro and published by . This book was released on 1969 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smoothing and Approximation of Functions written by Harold S. Shapiro (mathématicien).) and published by . This book was released on 1967 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smoothing and Approximation of Functions By Harold S Shapiro written by Harold S. Shapiro and published by . This book was released on 1969 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smoothing and Approximation of Functions Lectures Given in January February 1967 written by Harold S. Shapiro and published by . This book was released on 1967 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Splines and Their Applications written by J. H. Ahlberg and published by Elsevier. This book was released on 2016-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.
Download or read book Approximation of Real Smooth Functions written by Feng Dai and published by . This book was released on 2004 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smoothing and Approximation of Multivariate Functions written by E. W. Cheney and published by . This book was released on 1979 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the research project was to proceed as far as possible in the study of a certain class of practical approximation problems. Namely, the problem is to reduce the complexity of multivariate functions by representing them precisely or approximately by combinations of univariate functions. A prototype problem is that of finding a best approximation to a function of two variables, F(x, Y), by a sum g(x) + H(y). The prototype problem is thoroughly understood in the case that the functions involved are continuous and an approximation in the uniform sense is needed.
Download or read book Approximation of Functions written by Henry Leslie Garabedian and published by . This book was released on 1965 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Surface Approximation and Data Smoothing Using Generalized Spline Functions written by Gregory Morris Nielson and published by . This book was released on 1970 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation by Algebras of Smooth Functions written by Grayson K. Kakiko and published by . This book was released on 1998 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation of Functions written by G. G. Lorentz and published by American Mathematical Society. This book was released on 2023-05-08 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an easily accessible account of the approximation of functions. It is simple and without unnecessary details, but complete enough to include the classical results of the theory. With only a few exceptions, only functions of one real variable are considered. A major theme is the degree of uniform approximation by linear sets of functions. This encompasses approximations by trigonometric polynomials, algebraic polynomials, rational functions, and polynomial operators. The chapter on approximation by operators does not assume extensive knowledge of functional analysis. Two chapters cover the important topics of widths and entropy. The last chapter covers the solution by Kolmogorov and Arnol?d of Hilbert's 13th problem. There are notes at the end of each chapter that give information about important topics not treated in the main text. Each chapter also has a short set of challenging problems, which serve as illustrations.
Download or read book Approximation Theory Spline Functions and Applications written by S.P. Singh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the Proceedings of the NATO Advanced Study Institute on Approximation Theory, Spline Functions and Applications held in the Hotel villa del Mare, Maratea, Italy between April 28,1991 and May 9, 1991. The principal aim of the Advanced Study Institute, as reflected in these Proceedings, was to bring together recent and up-to-date developments of the subject, and to give directions for future research. Amongst the main topics covered during this Advanced Study Institute is the subject of uni variate and multivariate wavelet decomposition over spline spaces. This is a relatively new area in approximation theory and an increasingly impor tant subject. The work involves key techniques in approximation theory cardinal splines, B-splines, Euler-Frobenius polynomials, spline spaces with non-uniform knot sequences. A number of scientific applications are also highlighted, most notably applications to signal processing and digital im age processing. Developments in the area of approximation of functions examined in the course of our discussions include approximation of periodic phenomena over irregular node distributions, scattered data interpolation, Pade approximants in one and several variables, approximation properties of weighted Chebyshev polynomials, minimax approximations, and the Strang Fix conditions and their relation to radial functions. I express my sincere thanks to the members of the Advisory Commit tee, Professors B. Beauzamy, E. W. Cheney, J. Meinguet, D. Roux, and G. M. Phillips. My sincere appreciation and thanks go to A. Carbone, E. DePas cale, R. Charron, and B.
Download or read book An Introduction to the Approximation of Functions written by Theodore J. Rivlin and published by Courier Corporation. This book was released on 1981-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Theory of Approximation of Functions of a Real Variable written by A. F. Timan and published by Elsevier. This book was released on 2014-07-22 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.
Download or read book Numerical Methods of Statistics written by John F. Monahan and published by Cambridge University Press. This book was released on 2011-04-18 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.
Download or read book Approximation Theory and Methods written by M. J. D. Powell and published by Cambridge University Press. This book was released on 1981-03-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Extensions and Smooth Approximations of Definable Functions in O minimal Structures written by Athipat Thamrongthanyalak and published by . This book was released on 2013 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1934, H. Whitney presented a series of papers which discussed how to determine whether a function or a jet of order m is the restriction of a C^m function on R^n. In the first paper of the series, Whitney's Extension Theorem was proved. In the latter, Whitney answered special cases of the following question: Question. (Whitney's Extension Theorem, WEP_n, m) Let f be a continuous function from a closed subset of R^n. How can we determine whether f is the restriction of a C^m-function on R^n? In this dissertation, we work in o-minimal expansions of real closed ordered fields. Definable versions of Whitney's Extension Theorem and Whitney's Extension Problems will be discussed in this context. Definable set-valued maps are also studied; a definable version of Michael's Selection Theorem will be proved and used, in combination with a definable version of Whitney's Extension Theorem, to give a positive answer to a definable version of WEP_n,1. In addition to the above problems, we also discuss smoothing problems. This is inspired by a series of papers by A. Fischer. In this series, a construction of a definable C^m-approximation of a definable locally Lipschitz function is provided. Here, we also work in an o-minimal expansion of a real closed field and relax the condition further to just continuous.
