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The History of Approximation Theory: From Euler to Bernstein

The History of Approximation Theory: From Euler to Bernstein more books like this

by Karl-Georg Steffens, George A Anastassiou (Consultant editor)

The problem of approximating a given quantity is one of the oldest challenges faced by mathematicians. Its increasing importance in contemporary mathematics has created an entirely new area known as Approximation Theory. The modern theory was initially developed along two divergent schools of thought: the Eastern or Russian group, employing almost ...

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Best Approximation in Inner Product Spaces

Best Approximation in Inner Product Spaces more books like this

by Frank R Deutsch

This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book is some knowledge of advanced calculus and linear algebra. Throughout the book, examples ...

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Approximation Algorithms for Combinatorial Optimization

Approximation Algorithms for Combinatorial Optimization more books like this

by Klaus Jansen (Editor), Samir Khuller (Editor)

This book constitutes the refereed proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2000, held in Saarbrucken, Germany in September 2000. The 22 revised full papers presented together with four invited contributions were carefully reviewed and selected from 68 submissions. ...

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Approximation Methods for Electronic Filter Design: With Applications to Passive, Active, and Digital Networks more books like this

by Richard W Daniels

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Approximation Theory

Approximation Theory more books like this

by George A Anastassiou, Sorin G Gal

This monograph, in two parts, is an intensive and comprehensive study of the computational aspects of the moduli of smoothness and the Global Smoothness Preservation Property (GSPP). Key features include: systematic and extensive study of the computation of Moduli of Continuity and GSPP, presented for the first time in book form; substantial ...

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On L1-Approximation

On L1-Approximation more books like this

by Allan Pinkus

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. ...

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Selected Topics in Approximation and Computation

Selected Topics in Approximation and Computation more books like this

by Marek A. Kowalski, Krzysztof A. Sikorski, Frank Stenger

This graduate text addresses the relationship between modern approximation theory and computational methods. It is a combination of expositions of basic classical methods of approximation leading to popular splines and new explicit tools of computation, including sinc methods, elliptic function methods, and positive operator approximation methods. ...

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Tractable Reasoning in Aritificial Intelligence

Tractable Reasoning in Aritificial Intelligence more books like this

by Marco Cadoli

Logic is one of the most popular approaches to artificial intelligence. A potential obstacle to the use of logic is its high computational complexity, as logical inference is an extraordinarily powerful computational device.This book is concerned with computational aspects of the logical approach to AI. The focus is on two strategies for achieving ...

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Lectures on Proof Verification and Approximation Algorithms

Lectures on Proof Verification and Approximation Algorithms more books like this

by Ernst W Mayr (Editor), Hans Ja1/4rgen Pramel (Editor), Angelika Steger (Editor)

During the last few years, we have seen quite spectacular progress in the area of approximation algorithms: for several fundamental optimization problems we now actually know matching upper and lower bounds for their approximability. This textbook-like tutorial is a coherent and essentially self-contained presentation of the enormous recent ...

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Numerical Approximation of Partial Differential Equations

Numerical Approximation of Partial Differential Equations more books like this

by Alfio Quarteroni, Alberto Valli

This is the softcover reprint of the very popular hardcover edition. This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their ...

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Stochastic Approximation

Stochastic Approximation more books like this

by M T Wasan, Bela Bollobas (Editor), W Fulton (Editor)

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 ...

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Fractional Analysis more books like this

by Igor Novozhilov

Developed and implemented by the author, this text describes a method of constructing approximate math models of finite-dimensional dynamic systems. Fractional analysis is used as a mathematical tool of the proposed method. Fractional analysis unites algorithms of similitude and dimensionality theory and algorithms of asympototic expansions in ...

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Theory of Approximation more books like this

by N I Achieser, N I Akhiezer

Directed to advanced undergraduate and graduate students, approaching the subject from the viewpoint of functional analysis. Problems.

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An Introduction to the Approximation of Functions more books like this

by Theodore J. Rivlin

Concise, wide-ranging introduction to methods of approximating continuous functions depending only on a finite number of parameters. Emphasis on polynomials. Abundant excercises.

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Theory of Approximation of Functions of a Real Variable more books like this

by A F Timan

Excellent graduate-level monograph investigates relationship between real functions and polynomials and other functions of simple construction. Based upon theorems by Weierstrass, P. L. Chebyshev, S. N. Bernstein. Supplementary problems and theorems. 1963 edition.

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Semi-Classical Approximation in Quantum Mechanics more books like this

by Victor P Maslov, M V Fedoriuk

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Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates more books like this

by Pekka Neittaanmaki, Sergey Repin

Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods of reliable computations. In general, a reliable numerical method must solve two basic ...

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Approximation Theory and Methods more books like this

by M J D Powell

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 ...

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Harmonic Approximation more books like this

by Stephen J Gardiner

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 ...

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Order Stars: Theory and Applications more books like this

by A Iserles, Iserles Iserles, S P Norsett

Order stars is a recently developed technique to analyze and explain the behaviour of numerical methods. The main idea is to explore different features of numerical algorithms as properties of analytical functions in various portions of the complex plane. Thus, for example, the order of some numerical methods for ordinary differential equations ...

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Approximation of Elliptic Boundary-Value Problems more books like this

by Jean-Pierre Aubin

Mathematically self-contained, this text for advanced undergraduates and graduate students combines two important methods -- the finite element method and the variational method -- into the framework of functional analysis. It does so in order to explain potential applications to approximation of nonhomogeneous boundary-value problems for elliptic ...

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Topics in Multivariate Approximation and Interpolation more books like this

by Kurt Jetter (Editor), Werner Haussmann (Editor), Robert Schaback (Editor)

This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image ...

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Approximate calculation of integrals more books like this

by Vladimir Ivanovich Krylov

An introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. The 3-part treatment begins with concepts and theorems encountered in the theory of quadrature and then explores the problem of calculation of definite integrals and ...

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Approximation by Algebraic Numbers more books like this

by Yann Bugeaud

Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs. Starting from continued fractions and Khintchine's theorem, Bugeaud introduces a variety ...

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Biorthogonality and Its Applications to Numerical Analysis more books like this

by Claude Brezinski, Brezinski Brezinski

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