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On Variation Diminishing Spline Approximation Methods
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Book Synopsis On Variation Diminishing Spline Approximation Methods by : Martin J. Marsden
Download or read book On Variation Diminishing Spline Approximation Methods written by Martin J. Marsden and published by . This book was released on 1966 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Technical Summary Report 625 (AD-638 656) Schoenberg introduced a certain class of variation diminishing spline approximations which included as special cases the linear interpolation methods as well as the Bernstein polynomials. Concerning error bounds a few results were there only stated without proofs. Using a new identity for spline functions due to M. Marsden, the authors discuss here the question of convergence and also the closeness of individual approximations. The main result is that the spline approximations of low degree (cubic, for instance) have all the virtues of the linear interpolation method, while providing approximations having any desired number of continuous derivatives. (Author).
Book Synopsis An Identity for Spline Functions with Applications to Variation Diminishing Spline Approximation by : Martin J. Marsden
Download or read book An Identity for Spline Functions with Applications to Variation Diminishing Spline Approximation written by Martin J. Marsden and published by . This book was released on 1968 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: A spline function identity is developed and used to discuss the convergence properties of Schoenberg's variation diminishing spline approximation method. The Weierstrass approximation theorem is extended. Similar results for Chebshevian splines are developed. (Author).
Download or read book (1988). written by I. J. Schoenberg and published by Springer Science & Business Media. This book was released on 1988-06 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: These seleeta contain 761 of the more than 2600 pages of 1. J. Schoenberg's published articles. The selection made and the grouping in which the papers are presented here reflect most strongly Schoenberg's wishes. The first volume of these seleeta is drawn from Schoenberg's remarkable work on Number Theory, Positive Definite Functions and Metric Geometry, Real and Complex Analysis, and on the Landau Problem. Schoenberg's fundamental papers on Total Pos itivity and Variation Diminution, on P6lya Frequency functions and sequences, and on Splines, especially Cardinal Splines, make up the second volume. In addition, various commentaries have been provided. Lettered references in these refer to items listed alphabetically at the end of each commentary. Numbered references refer to the list of Schoenberg's publications to be found in each volume. Those included in these seleeta are starred. It has been an honor to have been entrusted with the editorial work for these seleeta. I am grateful to the writers of the various commentaries for their illuminating contributions and to Richard Askey for solid advice.
Book Synopsis Approximation Theory and Spline Functions by : S.P. Singh
Download or read book Approximation Theory and Spline Functions written by S.P. Singh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: A NATO Advanced Study Institute on Approximation Theory and Spline Functions was held at Memorial University of Newfoundland during August 22-September 2, 1983. This volume consists of the Proceedings of that Institute. These Proceedings include the main invited talks and contributed papers given during the Institute. The aim of these lectures was to bring together Mathematicians, Physicists and Engineers working in the field. The lectures covered a wide range including ~1ultivariate Approximation, Spline Functions, Rational Approximation, Applications of Elliptic Integrals and Functions in the Theory of Approximation, and Pade Approximation. We express our sincere thanks to Professors E. W. Cheney, J. Meinguet, J. M. Phillips and H. Werner, members of the International Advisory Committee. We also extend our thanks to the main speakers and the invi ted speakers, whose contri butions made these Proceedings complete. The Advanced Study Institute was financed by the NATO Scientific Affairs Division. We express our thanks for the generous support. We wish to thank members of the Department of Mathematics and Statistics at MeMorial University who willingly helped with the planning and organizing of the Institute. Special thanks go to Mrs. Mary Pike who helped immensely in the planning and organizing of the Institute, and to Miss Rosalind Genge for her careful and excellent typing of the manuscript of these Proceedings.
Book Synopsis On Spline Functions by : I. J. Schoenberg
Download or read book On Spline Functions written by I. J. Schoenberg and published by . This book was released on 1966 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown how spline functions allow one to generalize the Bernstein polynomials, thereby also leading to variation diminishing approximation methods which converge faster than the Bernstein polynomials. (Author).
Book Synopsis Splines and Variational Methods by : P. M. Prenter
Download or read book Splines and Variational Methods written by P. M. Prenter and published by Courier Corporation. This book was released on 2013-11-26 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text’s first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.
Book Synopsis Methods of Shape-preserving Spline Approximation by : Boris I. Kvasov
Download or read book Methods of Shape-preserving Spline Approximation written by Boris I. Kvasov and published by World Scientific. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces. Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.
Book Synopsis Spline Functions: Basic Theory by : Larry Schumaker
Download or read book Spline Functions: Basic Theory written by Larry Schumaker and published by Cambridge University Press. This book was released on 2007-08-16 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.
Book Synopsis On the Approximation of Multivariate Functions by : Gh Coman
Download or read book On the Approximation of Multivariate Functions written by Gh Coman and published by . This book was released on 1974 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the report is to study the remainder term of Schoenberg's variation diminishing spline approximation formula and to extend some univariate results to the approximation of multivariate functions. Also, a method is described which obtains multivariate numerical approximation schemes with a higher order of approximation. Finally, some illustrative examples are included. (Modified author abstract).
Book Synopsis Handbook of Splines by : Gheorghe Micula
Download or read book Handbook of Splines written by Gheorghe Micula and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.
Book Synopsis Approximation Theory and Methods by : M. J. D. Powell
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.
Book Synopsis Spline and Spline Wavelet Methods with Applications to Signal and Image Processing by : Amir Z. Averbuch
Download or read book Spline and Spline Wavelet Methods with Applications to Signal and Image Processing written by Amir Z. Averbuch and published by Springer. This book was released on 2018-06-19 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a practical guide, complete with accompanying Matlab software, to many different types of polynomial and discrete splines and spline-based wavelets, multiwavelets and wavelet frames in signal and image processing applications. In self-contained form, it briefly outlines a broad range of polynomial and discrete splines with equidistant nodes and their signal-processing-relevant properties. In particular, interpolating, smoothing, and shift-orthogonal splines are presented.
Book Synopsis Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters by : Nitta, Tohru
Download or read book Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters written by Nitta, Tohru and published by IGI Global. This book was released on 2009-02-28 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book covers the current state-of-the-art theories and applications of neural networks with high-dimensional parameters"--Provided by publisher.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis I. J. Schoenberg Selected Papers by : Boor
Download or read book I. J. Schoenberg Selected Papers written by Boor and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asian and Pacific Coasts 2003 by : Yoshimi Goda
Download or read book Asian and Pacific Coasts 2003 written by Yoshimi Goda and published by World Scientific. This book was released on 2004 with total page 1583 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the experience of coastal and port engineering development, as well as coastal environmental problems, in Asian and Pacific countries. It also provides information and promotes technological progress and activities, international technical transfer and cooperation, and opportunities for engineers and researchers to maintain and improve scientific and technical competence. The subject areas are not limited to the classical topics of coastal engineering but are extended to related fields, including environments, marine ecology, coastal oceanography, fishery, etc.
Book Synopsis Government-wide Index to Federal Research & Development Reports by :
Download or read book Government-wide Index to Federal Research & Development Reports written by and published by . This book was released on 1967 with total page 1234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
