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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 series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. The book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related application areas. It contains a carefully refereed and edited selection of papers. Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research.  Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation.  Marian Neamtu is Professor of Mathematics at Vanderbilt University, Nashville, TN.  Larry L. Schumaker is Stevenson Professor of Mathematics at Vanderbilt University, Nashville, TN.

Approximation theory -- Congresses. --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Algebra --- Operations Research --- Approximation theory --- Mathematics. --- Approximation theory. --- Computer mathematics. --- Approximations and Expansions. --- Computational Mathematics and Numerical Analysis. --- Computer science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems

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Mathematical analysis --- Numerical approximation theory --- Approximation theory --- Functional analysis --- Congresses --- 517.98 --- -Functional analysis --- -517.518.8 --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- Functional analysis and operator theory --- Approximation of functions by polynomials and their generalizations --- 517.518.8 Approximation of functions by polynomials and their generalizations --- 517.98 Functional analysis and operator theory --- 517.518.8 --- Approximation theory - Congresses --- Functional analysis - Congresses

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Approximation theory --- Spline theory --- Théorie de l'approximation --- Splines, Théorie des --- Congresses --- Congrès --- Congresses. --- -Spline theory --- -517.518.8 --- Spline functions --- Interpolation --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Approximation of functions by polynomials and their generalizations --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Théorie de l'approximation --- Splines, Théorie des --- Congrès --- 517.518.8 --- Approximation, Théorie de l' --- Approximation, Théorie de l' --- Splines. --- Approximation theory - Congresses. --- Spline theory - Congresses.

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Numerical approximation theory --- Approximation theory --- Functions of several real variables --- Functions of several complex variables --- Congresses --- 519.6 --- 681.3*G12 --- Computational mathematics. Numerical analysis. Computer programming --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Real variables --- Several real variables, Functions of --- Functions of real variables --- Approximation theory - Congresses --- Functions of several real variables - Congresses --- Functions of several complex variables - Congresses

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Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to the renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines. - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in engineering and other computational and applied sciences.

Approximation theory -- Congresses. --- Approximation theory -- Data processing -- Congresses. --- Numerical integration -- Congresses. --- Orthogonal polynomials -- Congresses. --- Approximation theory --- Numerical analysis --- Mathematics --- Civil & Environmental Engineering --- Algebra --- Operations Research --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Approximation theory. --- Numerical analysis. --- Milovanović, G. V. --- Theory of approximation --- Milovanović, Gradimir V. --- Mathematics. --- Computer science --- Computer mathematics. --- Mathematical optimization. --- Optimization. --- Computational Mathematics and Numerical Analysis. --- Approximations and Expansions. --- Mathematics of Computing. --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Mathematical analysis --- Computer science. --- Informatics --- Science --- Math --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Computer science—Mathematics. --- Milovanovic, G. V.