Constructive Approximation

This and the earlier book by R.A. DeVore and G.G. Lorentz (Vol. 303 of the same series), cover the whole field of approximation of functions of one real variable. The main subject of this volume is ap

本書《當X世代遇到Z世代的大學教學》探討當前「X世代」的大學教師，如何在面對「Z 世代」時，冒著可能被學生申訴的風險，完成愈來愈艱難的教學任務。 隨著網路科技的快速進展，當前全世界的大學都面臨到這群在學習方式、語言表達、認知思維、價值觀、行為模式、人際關係，甚至情緒管理等，都與以往截然不同的新新人類。面對他們常年活躍於網路世界，大學課堂如何留住他們的「人」與「心」，的確是個新課題。透過作者多年的觀察及教學經驗，經由一些精彩的案例，與讀者分享。 This book attempts to showcase how university teaching is in great transition owing to the unprecedented presence of Gen Z on campus. The author argues that both Gen X and Gen Z need to understand and accept each other, so university teaching can take place in a more effective and constructive way. 上大學到底為了什麼? 現在的大學生有什麼不一樣? 大學教授如何面對網路世代? X世代遇到Z世代會迸出什麼火花?

This book is the first one that gives a systematic presentation of recent fundamental results on greedy approximation with respect to bases. Greedy approximation is a very fresh area of research where

Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation proper

Originally published in 1987, this book is devoted to the approximation of real functions by real rational functions. These are, in many ways, a more convenient tool than polynomials, and interest in them was growing, especially since D. Newman's work in the mid-sixties. The authors aim at presenting the basic achievements of the subject and, for completeness, also discuss some topics from complex rational approximation. Certain classical and modern results from linear approximation theory and spline approximation are also included for comparative purposes. This book will be of value to anyone with an interest in approximation theory and numerical analysis.

This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-w

This monograph is concerned with the qualitative theory of best L1-approximation from finite-dimensional subspaces. It presents a survey of recent research that extends 'classical' results concerned with best uniform approximation to the L1 case. The work is organized in such a way as to be useful for self-study or as a text for advanced courses. It begins with a basic introduction to the concepts of approximation theory before addressing one- or two-sided best approximation from finite-dimensional subspaces and approaches to the computation of these. At the end of each chapter is a series of exercises; these give the reader an opportunity to test understanding and also contain some theoretical digressions and extensions of the text.

The subject of harmonic approximation has recently matured into a coherent research area with extensive applications. This is the first book to give a systematic account of these developments, beginning with classical results concerning uniform approximation on compact sets, and progressing through fusion techniques to deal with approximation on unbounded sets. All the time inspiration is drawn from holomorphic results such as the well-known theorems of Runge and Mergelyan. The final two chapters deal with wide-ranging and surprising applications to the Dirichlet problem, maximum principle, Radon transform and the construction of pathological harmonic functions. This book is aimed at graduate students and researchers who have some knowledge of subharmonic functions, or an interest in holomorphic approximation.

This book provides a systematic survey of classical and recent results on hyperbolic cross approximation. Motivated by numerous applications, the last two decades have seen great success in studying m

Constructive Nonlinear Control presents a broad repertoire of constructive nonlinear designs not available in other works by widening the class of systems and design tools. Several streams of nonlinea

This book constitutes the joint refereed proceedings of the 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012, and the 16th International Wor

This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts conc

First published in 1987, Constructive Drinking is a series of original case studies organized into three sections based on three major functions of drinking. The three constructive functions are: that

Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to suppo

This concisely written book gives an elementary introduction to a classical area of mathematics - approximation theory - in a way that naturally leads to the modern field of wavelets. The ex

This book presents the recent development of stochastic approximation algorithms with expanding truncations based on the TS (trajectory-subsequence) method, a newly developed method for convergence an

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 mathematic

This volume demonstrates how Friedrich Schleiermacher’s thought can be used to address contemporary doctrinal refinement and development. Taking a constructive approach, Shelli M. Poe weaves Schleiermacher’s theology together with current scholarship in feminism, womanism, ecotheology, and queer theology. While Schleiermacher is widely acclaimed as the progenitor of modern theology, Poe is one of the first to use his work as a springboard to refine contemporary doctrine. This book demonstrates the promise of Schleiermacher’s mature work for contemporary constructive forms of theology.

The Constructive Mind is an integrative study of the psychologist Frederic Bartlett's (1886–1969) life, work and legacy. Bartlett is most famous for the idea that remembering is constructive and for the concept of schema; for him, 'constructive' meant that human beings are future-oriented and flexibly adaptive to new circumstances. This book shows how his notion of construction is also central to understanding social psychology and cultural dynamics, as well as other psychological processes such as perceiving, imagining and thinking. Wagoner contextualises the development of Bartlett's key ideas in relation to his predecessors and contemporaries. Furthermore, he applies Bartlett's constructive analysis of cultural transmission in order to chart how his ideas were appropriated and transformed by others that followed. As such this book can also be read as a case study in the continuous reconstruction of ideas in science.

This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Val

Asian Martial Arts: Constructive Thoughts & Practical Applications represents an international gathering of friends who happen to be highly qualified marital art scholars and practitioners. This marti

Constructive Conflicts provides a framework for analyzing social conflicts of all kinds, with emphasis on how conflicts can lead to positive change. The fifth edition features new material on the role

The proceedings of the third annual Los Angeles Theology Conference seek to identify the place of the doctrine of atonement in systematic theology.Locating Atonement: Explorations in Constructive Dogm

Constructive Clinical Supervision in Counseling and Psychotherapy articulates a practical, theoretical approach to supervision that integrates salient elements of a number of diverse but complementary

?Constructive wallowing” seems like an oxymoron. Constructive is a good thing, but wallowing is bad. Right?But wait a minute; is it really so terrible to give ourselves a time-out to feel our feelings

The papers in this volume were presented at an International Symposium on Optimal Estimation in Approximation Theory which was held in Freudenstadt, Federal Republic of Germany, September 27-29, 1976.

In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes conside

??????This book is devoted to fully developing and comparing the two main approaches to the numerical approximation of controls for wave propagation phenomena: the continuous and the discrete. This is

This book constitutes the refereed proceedings of the Third International Workshop on Constructive Side-Channel Analysis and Secure Design, COSADE 2012, held in Darmstadt, Germany, May 2012.The 16 rev

In recent years important progress has been made in the study of semi-groups of operators from the viewpoint of approximation theory. These advances have primarily been achieved by introducing the the

This book constitutes the joint refereed proceedings of the 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010, and the 14th International Wor

Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and method

This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximation

Academics and practitioners consider various aspects of a constructive approach to working with criminal offenders. The volume begins with an overview of recent trends in the criminal justice system i

This book constitutes the joint refereed proceedings of the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and the 9th International Worksh

This work treats quantitative aspects of the approximation of functions using positive linear operators. The theory of these operators has been an important area of research in the last few decades, p

Stochastic approximation is a relatively new technique for studying the properties of an experimental situation; it has important applications in fields such as medicine and engineering. The subject can be treated either largely as a branch of pure mathematics, or else from an empirical and practical angle. In this book, Dr Wasan gives a rigorous mathematical treatment of the subject, drawing together the scattered results of a number of authors. He discusses the conditions under which the method gives a valid approximation to the required solution; methods for optimal choice of parameters to hasten convergence; the comparison of the method with other techniques. The discussion and proofs of theorems are given in enough detail to make them easy to follow, while a number of interesting examples show how the techniques may be applied in many fields.

Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.

This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.

A guide to healing our fractured discourse on race and racism by having better arguments―as in, actually constructive and enriching arguments, rather than shouting matches or personal attacksFrom a sc