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"Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships. A mapping principle is presented to connect many of the methods. The eigenvalue problems studied are linear, and linearization is shown to give important information about nonlinear problems. Linear vector spaces and their properties are used to uniformly describe the eigenvalue problems presented that involve matrices, ordinary or partial differential operators, and integro-differential operators."

"In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications."

"Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational, accuracy, and storage capabilities, model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications."

"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."

"Contains the proceedings that were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas. This book includes many relevant topics in approximation theory, such as abstract approximation, approximation with constraints, and interpolation and smoothing."

"The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra. The topics include polynomial interpolation, Bernstein polynomials and the Weierstrass theorem, best approximations in the general setting of normed linear spaces and inner product spaces, best uniform polynomial approximation, orthogonal polynomials, Newton-Cotes , Gauss and Clenshaw-Curtis quadrature, the Euler-Maclaurin formula, approximation of periodic functions, the uniform convergence of Fourier series, spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter."