On L1 Approximation
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| Author | : Allan Pinkus |
| Publisher | : Cambridge University Press |
| Total Pages | : 253 |
| Release | : 1989 |
| Genre | : Mathematics |
| ISBN | : 052136650X |
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.
| Author | : |
| Publisher | : Academic Press |
| Total Pages | : 573 |
| Release | : 2011-09-21 |
| Genre | : Mathematics |
| ISBN | : 0080873537 |
Fourier Analysis and Approximation
| Author | : Nabih Abdelmalek |
| Publisher | : CRC Press |
| Total Pages | : 964 |
| Release | : 2008-05-19 |
| Genre | : Mathematics |
| ISBN | : 1584889780 |
Illustrating the relevance of linear approximation in a variety of fields, Numerical Linear Approximation in C presents a unique collection of linear approximation algorithms that can be used to analyze, model, and compress discrete data. Developed by the lead author, the algorithms have been successfully applied to several engineering projects at the National Research Council of Canada. Basing most of the algorithms on linear programming techniques, the book begins with an introductory section that covers applications, the simplex method, and matrices. The next three parts focus on various L1, Chebyshev, and least squares approximations, including one-sided, bounded variables, and piecewise. The final section presents the solution of underdetermined systems of consistent linear equations that are subject to different constraints on the elements of the unknown solution vector. Except in the preliminary section, all chapters include the C functions of the algorithms, along with drivers that contain numerous test case examples and results. The accompanying CD-ROM also provides the algorithms written in C code as well as the test drivers. To use the software, it is not required to understand the theory behind each function.
| Author | : Vašek Chvátal |
| Publisher | : Macmillan |
| Total Pages | : 500 |
| Release | : 1983-09-15 |
| Genre | : Mathematics |
| ISBN | : 9780716715870 |
"This comprehensive treatment of the fundamental ideas and principles of linear programming covers basic theory, selected applications, network flow problems, and advanced techniques. Using specific examples to illuminate practical and theoretical aspects of the subject, the author clearly reveals the structures of fully detailed proofs. The presentation is geared toward modern efficient implementations of the simplex method and appropriate data structures for network flow problems. Completely self-contained, it develops even elementary facts on linear equations and matrices from the beginning."--Back cover.
| Author | : Kazuaki Kitahara |
| Publisher | : Springer |
| Total Pages | : 119 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540484043 |
Tchebycheff (or Haar) and weak Tchebycheff spaces play a central role when considering problems of best approximation from finite dimensional spaces. The aim of this book is to introduce Haar-like spaces, which are Haar and weak Tchebycheff spaces under special conditions. It studies topics of subclasses of Haar-like spaces, that is, classes of Tchebycheff or weak Tchebycheff spaces, spaces of vector-valued monotone increasing or convex functions and spaces of step functions. The notion of Haar-like spaces provides a general point of view which includes the theories of approximation from the above spaces. The contents are largely new. Graduate students and researchers in approximation theory will be able to read this book with only basic knowledge of analysis, functional analysis and linear algebra.
| Author | : M. J. D. Powell |
| Publisher | : Cambridge University Press |
| Total Pages | : 356 |
| Release | : 1981-03-31 |
| Genre | : Mathematics |
| ISBN | : 9780521295147 |
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.
| Author | : Zhi-Zhong Sun |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 396 |
| Release | : 2020-08-24 |
| Genre | : Mathematics |
| ISBN | : 3110616068 |
Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.
| Author | : Werner Haussmann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 324 |
| Release | : 2003-10-24 |
| Genre | : Mathematics |
| ISBN | : 9783764321956 |
This volume contains a selection of eighteen peer-reviewed articles that were presented at the 5th International Conference on Multivariate Approximation, held in Witten-Bommerholz in September 2002. The contributions cover recent developments of constructive approximation on manifolds, approximation by splines and kernels, subdivision techniques and wavelet methods. The main topics are: - applications of multivariate approximation in finance - approximation and stable reconstruction of images, data reduction - multivariate splines for Lagrange interpolation and quasi-interpolation - radial basis functions - spherical point sets - refinable function vectors and non-stationary subdivision - applications of adaptive wavelet methods - blending functions and cubature formulae - singularities of harmonic functions The book provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics, with many links to computer science and geophysics.
| Author | : C. Brezinski |
| Publisher | : Elsevier |
| Total Pages | : 512 |
| Release | : 2012-12-02 |
| Genre | : Mathematics |
| ISBN | : 0444598588 |
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.
| Author | : Changpin Li |
| Publisher | : SIAM |
| Total Pages | : 327 |
| Release | : 2019-10-31 |
| Genre | : Mathematics |
| ISBN | : 1611975883 |
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.
