Computational Integration

Computational Integration is the first book in over 10 years dedicated to a comprehensive discussion of computational integration methods and the fundamental mathematical principles they are based on. It gives special coverage of many recent developments, such as parallel integration algorithms, that have not yet been coherently presented in any other textbook. It also attempts to bridge the gap between theoretical knowledge about and practical application of computational integration by providing references to and descriptions of numerous relevant software products.

This survey covers a wide range of topics fundamental to calculating integrals on computer systems and discusses both the theoretical and computational aspects of numerical and symbolic methods. It includes extensive sections on one- and multidimensional integration formulas, like polynomial, number-theoretic, and pseudorandom formulas, and deals with issues concerning the construction of numerical integration algorithms, including error estimation, discretization refinement, and convergence acceleration. Individual chapters are dedicated to parallel integration algorithms, the assessment of numerical integration software, and numerical methods tailored to particular kinds of integration problems involving, for instance, oscillatory or singular integrands.