Approximation

This book is intended to be used as a textbook for graduate students studying theoretical computer science. It can also be used as a reference book for researchers in the area of design and analysis o

This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fract

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely

This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral powers of 3/2 and the frequency of occurrence of each digit in the decimal expansion of the square root of two. The author takes a point of view from combinatorics on words and introduces a variety of techniques, including explicit constructions of normal numbers, Schmidt's games, Riesz product measures and transcendence results. With numerous exercises, the book is ideal for graduate courses on Diophantine approximation or as an introduction to distribution modulo one for non-experts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references.

These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7–10, 2010 in San Antonio, Texas. The conference was the thirteenth in a

In this Spanish bestseller, now available in English for the first time, the famous Biblical scholar Jose Antonio Pagola reconstructs the historical Jesus with a scholarly exegetical and theological

Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov

This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material o

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

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

Surveys the enormous literature on numerical approximation of solutions of elliptic boundary problems by means of variational and finite element methods, requiring almost constant application of resul

Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, the

This is the third of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses topics that depend more on calculus than linear algebra, in

This textbook provides students with a solid introduction to the techniques of approximation commonly used in data analysis across physics and astronomy. The choice of methods included is based o

This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method a

This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods.

Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of r

This book offers advanced graduates and researchers a trove of key results in the study of convergence, in both real and complex domains. It explores new and more efficient applications developed by t

The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested research

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

Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. This volume contains thorough coverage of the method’s fundamentals. It includes a large number of

In recent years the traditional subject of continuum mechanics has grown rapidly and many new techniques have emerged. This text provides a rigorous, yet accessible introduction to the basic concepts of the network approximation method and provides a unified approach for solving a wide variety of applied problems. As a unifying theme, the authors discuss in detail the transport problem in a system of bodies. They solve the problem of closely placed bodies using the new method of network approximation for PDE with discontinuous coefficients, developed in the 2000s by applied mathematicians in the USA and Russia. Intended for graduate students in applied mathematics and related fields such as physics, chemistry and engineering, the book is also a useful overview of the topic for researchers in these areas.

Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provid

Asymptotic techniques have long been important in statistical inference; these techniques remain important in the age of fast computing because some exact answers are still either conceptually unavail

This monograph addresses the problem of "real-time" curve fitting in the presence of noise, from the computational and statistical viewpoints. It examines the problem of nonlinear regression, where ob

This book addresses the formulation, approximation and numerical solution of optimal shape design problems: from the continuous model through its discretization and approximation results, to sensitivi