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Vladimir Temlyakov guides the reader through the fundamental results and introduces two other hot topics in numerical mathematics: learning theory and compressed sensing. Researchers will welcome this first book on the subject. It is ideal for graduate courses and includes many important open problems that provide ideas for further research.

Very much a users-guide, this book provides insight to the use of preconditioning techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems from electrical power stations. Supporting MATLAB files are available via the Web to assist and develop readers' understanding, and provide stimulus for further study.

This book explains and develops new applications of continuous symmetry groups (Lie groups), in particular, the symbolic manipulation of invariants of group actions. The language used is primarily that of undergraduate calculus. More sophisticated ideas from differential topology and Lie theory are explained from scratch using worked examples and exercises.

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models are singular: mixture models, neural networks, HMMs, and Bayesian networks are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.

The goal of learning theory is to approximate a function from sample values. This is a general overview of the theoretical foundations, and is the first book to emphasize the approximation theory viewpoint. This emphasis provides a balanced approach, and will attract mathematicians to the problems raised.

Linked Twist Maps can provide a unifying framework for understanding many types of fluid mixing, ranging from the very small to the very large, from fluids to solids. The authors discuss the definition and construction of LTMs, provide examples of specific mixers, and present a number of open problems.

A comprehensive look at the Schwarz-Christoffel transformation, including its many applications.

This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods.