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This book deals with various aspects of scientific numerical computing. No at­ tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli­ cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous.

Numerical analysis --- Computer science --- Analyse numérique --- Data processing. --- Informatique --- Engineering & Applied Sciences --- Applied Mathematics --- Analyse numérique --- Numerical analysis. --- Algorithms. --- Computer science—Mathematics. --- Computational intelligence. --- Numerical Analysis. --- Mathematics of Computing. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Algorism --- Algebra --- Arithmetic --- Mathematical analysis --- Foundations --- Analyse numérique.

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This monograph is a comprehensive treatment of the theoretical and computational aspects of numerical integration. The authors give a unique overview of the topic by bringing into line many recent research results not yet presented coherently; the extensive bibliography lists 268 items. Particular emphasis is given to the potential parallelism of numerical integration problems and to utilizing it by means of dynamic load distribution techniques. The book discusses the basics and provides methodologies for producing efficient and reliable software for numerical integration on advanced computer systems. The book addresses researchers, graduate students, and computational scientists.

Numerical analysis --- Computer. Automation --- Numerical integration --- -519.6 --- 681.3*G14 --- 681.3*G4 --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Data processing --- Computational mathematics. Numerical analysis. Computer programming --- Quadrature and numerical differentiation: adaptive quadrature; equal intervalintegration; error analysis; finite difference methods; gaussian quadrature; iterated methods; multiple quadrature --- Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- 681.3*G4 Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- 681.3*G14 Quadrature and numerical differentiation: adaptive quadrature; equal intervalintegration; error analysis; finite difference methods; gaussian quadrature; iterated methods; multiple quadrature --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Numerical integration - Data processing. --- Information theory. --- Numerical analysis. --- Algorithms. --- Theory of Computation. --- Numerical Analysis. --- Algorism --- Algebra --- Arithmetic --- Mathematical analysis --- Communication theory --- Communication --- Cybernetics --- Foundations