Download or read book On L1 Approximation written by Allan Pinkus and published by Cambridge University Press. This book was released on 1989 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses the qualitative linear theory of best L^T1-approximation from finite-dimensional subspaces. It presents a survey of recent research that extends "classical" results concerned with best-uniform approximation to the more general case. The work is organized to serve as a self-study guide or as a text for advanced courses. It begins with a basic introduction to the concepts of approximation theory before addressing 1- or 2-sided best approximations from finite-dimensional subspaces and approaches to the computation of these. At the end of each chapter is a series of exercises that give the reader an opportunity to test understanding and also contain some theoretical digressions and extensions of the text.
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 Periodic Integral and Pseudodifferential Equations with Numerical Approximation written by Jukka Saranen and published by Springer Science & Business Media. This book was released on 2001-11-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
Download or read book Analytical and Approximate Methods written by Hans-Peter Blatt and published by . This book was released on 2003 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiscale Nonlinear and Adaptive Approximation written by Ronald DeVore and published by Springer Science & Business Media. This book was released on 2009-09-16 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book of invited articles offers a collection of high-quality papers in selected and highly topical areas of Applied and Numerical Mathematics and Approximation Theory which have some connection to Wolfgang Dahmen's scientific work. On the occasion of his 60th birthday, leading experts have contributed survey and research papers in the areas of Nonlinear Approximation Theory, Numerical Analysis of Partial Differential and Integral Equations, Computer-Aided Geometric Design, and Learning Theory. The main focus and common theme of all the articles in this volume is the mathematics building the foundation for most efficient numerical algorithms for simulating complex phenomena.
Download or read book Theory and Numerical Approximations of Fractional Integrals and Derivatives written by Changpin Li and published by SIAM. This book was released on 2019-10-31 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus, provides a detailed treatment of existing numerical approximations, and presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results. The core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.
Download or read book The Mathematical Heritage of C F Gauss written by George M. Rassias and published by World Scientific. This book was released on 1991-09-01 with total page 930 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of original and expository papers in the fields of Mathematics in which Gauss had made many fundamental discoveries. The contributors are all outstanding in their fields and the volume will be of great interest to all research mathematicians, research workers in the history of science, and graduate students in Mathematics and Mathematical Physics.
Download or read book Numerical Treatment and Analysis of Time Fractional Evolution Equations written by Bangti Jin and published by Springer Nature. This book was released on 2023-02-26 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis.
Download or read book Splines and PDEs From Approximation Theory to Numerical Linear Algebra written by Angela Kunoth and published by Springer. This book was released on 2018-09-20 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.
Download or read book Approximation Theory Sequence Spaces and Applications written by S. A. Mohiuddine and published by Springer Nature. This book was released on 2022-12-07 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Theory written by George Anastassiou and published by CRC Press. This book was released on 1992-04-24 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Algorithmic Learning Theory written by Yoav Freund and published by Springer Science & Business Media. This book was released on 2008-09-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th International Conference on Algorithmic Learning Theory, ALT 2008, held in Budapest, Hungary, in October 2008, co-located with the 11th International Conference on Discovery Science, DS 2008. The 31 revised full papers presented together with the abstracts of 5 invited talks were carefully reviewed and selected from 46 submissions. The papers are dedicated to the theoretical foundations of machine learning; they address topics such as statistical learning; probability and stochastic processes; boosting and experts; active and query learning; and inductive inference.
Download or read book Recent Progress in Multivariate Approximation written by Werner Haussmann and published by Springer Science & Business Media. This book was released on 2001 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the main results of the 4th International Conference on Multivariate Approximation, which was held at Witten-Bommerholz, September 24-29, 2000. Nineteen selected, peer-reviewed contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision. Features and Topics: interpolation and approximation on compact sets, kergin interpolationerror asymptoticsradial basis functionsenergy minimizing configurations on the spherequadrature and cubature formulaeharmonic functions near a zeroblending functionsframes and approximation of inverse frame operators The book is an essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.
Download or read book n Widths in Approximation Theory written by A. Pinkus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: My original introduction to this subject was through conservations, and ultimate ly joint work with C. A. Micchelli. I am grateful to him and to Profs. C. de Boor, E. W. Cheney, S. D. Fisher and A. A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction . . . . . . . . Chapter II. Basic Properties of n-Widths . 9 1. Properties of d • • • • • • • • • • 9 n 15 2. Existence of Optimal Subspaces for d • n n 17 3. Properties of d • • • • • • 20 4. Properties of b • • • • • • n 5. Inequalities Between n-Widths 22 n 6. Duality Between d and d • • 27 n 7. n-Widths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References . . . . . . . . . . . . . .
Download or read book String Processing and Information Retrieval written by Amihood Amir and published by Springer. This book was released on 2008-11-14 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th International Symposium on String Processing and Information Retrieval, SPIRE 2008, held in Melbourne, Australia, in November 2008. The 25 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 54 submissions. The papers are organized in topical sections on compression and performance, information retrieval scoring and ranking, string matching techniques, self-indexing, string matching: space and practicality, information retrieval, non-standard matching, and bioinformatics.
Download or read book SIAM Journal on Numerical Analysis written by and published by . This book was released on 1979 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains research articles on the development and analysis of numerical methods, including their convergence, stability, and error analysis as well as related results in functional analysis and approximation theory. Computational experiments and new types of numerical applications are also included.
