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'Selected Topics in Approximation and Computation' 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. It also provides an excellent summary of worst case analysis in information based complexity. It relates optimal computational methods e=with the theory of s-numbers and m-widths.

Approximation theory. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems

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The key point of the monograph is the classification of periodic functions introduced by the author and developed methods that enable one to solve, within the framework of a common approach, traditional problems of approximation theory for large collections of periodic functions. The main results are fairly complete and are presented in the form of either exact or asymptotically exact equalities. The present monograph is, in many respects, a store of knowledge accumulated in approximation theory by the beginning of the third millennium and serving for its further development.

Approximation theory. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems

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The book "Computational Error and Complexity in Science and Engineering? pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will t

Engineering mathematics. --- Approximation theory. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics

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Stein's method is a collection of probabilistic techniques that allow one to assess the distance between two probability distributions by means of differential operators. In 2007, the authors discovered that one can combine Stein's method with the powerful Malliavin calculus of variations, in order to deduce quantitative central limit theorems involving functionals of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space. Many recent developments and applications are studied in detail, for instance: fourth moment theorems on the Wiener chaos, density estimates, Breuer-Major theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely self-contained, the book is perfect for self-study. It will appeal to researchers and graduate students in probability and statistics, especially those who wish to understand the connections between Stein's method and Malliavin calculus.

Approximation theory. --- Malliavin calculus. --- Calculus, Malliavin --- Stochastic analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Analyse stochastique

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The Special Functions and Their Approximations: v. 1

Approximation theory. --- Functions, Special. --- Heat -- Radiation and absorption. --- Materials -- Thermal properties. --- Special functions --- Theory of approximation --- Mathematical analysis --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems