Mathematics of Computing -- Numerical Analysis.

This revised edition provides the mathematical background and algorithmic skills required for the production of numerical software. It includes rewritten and clarified proofs and derivations, as well as new topics such as Arnoldi iteration, and domain decomposition methods.

High technology industries are in desperate need for adequate tools to assess the validity of simulations produced by ever faster computers for perennial unstable problems. In order to meet these industrial expectations, applied mathematicians are facing a formidable challenge summarized by these words — nonlinearity and coupling. This book is unique as it proposes truly original solutions: (1) Using hypercomputation in quadratic algebras, as opposed to the traditional use of linear vector spaces in the 20th century; (2) complementing the classical linear logic by the complex logic which expresses the creative potential of the complex plane.The book illustrates how qualitative computing has been the driving force behind the evolution of mathematics since Pythagoras presented the first incompleteness result about the irrationality of √2. The celebrated results of Gödel and Turing are but modern versions of the same idea: the classical logic of Aristotle is too limited to capture the dynamics of nonlinear computation. Mathematics provides us with the missing tool, the organic logic, which is aptly tailored to model the dynamics of nonlinearity. This logic will be the core of the “Mathematics for Life” to be developed during this century.

Enabling Technologies for Computational Science assesses future application computing needs, identifies research directions in problem-solving environments (PSEs), addresses multi-disciplinary environments operating on the Web, proposes methodologies and software architectures for building adaptive and human-centered PSEs, and describes the role of symbolic computing in scientific and engineering PSEs. The book also includes an extensive bibliography of over 400 references. Enabling Technologies for Computational Science illustrates the extremely broad and interdisciplinary nature of the creation and application of PSEs. Authors represent academia, government laboratories and industry, and come from eight distinct disciplines (chemical engineering, computer science, ecology, electrical engineering, mathematics, mechanical engineering, psychology and wood sciences). This breadth and diversity extends into the computer science aspects of PSEs. These papers deal with topics such as artificial intelligence, computer-human interaction, control, data mining, graphics, language design and implementation, networking, numerical analysis, performance evaluation, and symbolic computing. Enabling Technologies for Computational Science provides an assessment of the state of the art and a road map to the future in the area of problem-solving environments for scientific computing. This book is suitable as a reference for scientists from a variety of disciplines interested in using PSEs for their research.

Surveys and summaries of latest research in numerical analysis, optimization, computer algebra and scientific computing.

Numerical software is central to our computerized society. It is used to control aeroplanes and bridges, operate manufacturing lines, control power plants and refineries, and analyse financial markets. Such software must be accurate, reliable, robust, efficient, easy to use, maintainable and adaptable. Quality assessment and control of numerical software is still not well understood. Although measurement is a key element, it remains difficult to assess many components of software quality and to evaluate the trade-offs between them. Fortunately, as numerical software is built upon a long established foundation of mathematical and computational knowledge, there is great potential for dramatic breakthroughs. This volume will address enabling techniques and tools such as benchmarks, testing methodologies, quality standards, metrics, and accuracy control mechanisms, and their application to software for differential equations, linear algebra, data analysis, as well as the evaluation of integrals, derivatives and elementary and special functions.

Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.

This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on High Performance Computing for Computational Science, VECPAR 2008, held in Toulouse, France, in June 2008. The 51 revised full papers presented together with the abstract of a surveying and look-ahead talk were carefully reviewed and selected from 73 submissions. The papers are organized in topical sections on parallel and distributed computing, cluster and grid computing, problem solving environment and data centric, numerical methods, linear algebra, computing in geosciences and biosciences, imaging and graphics, computing for aerospace and engineering, and high-performance data management in grid environments.

ETAPS2002wasthe?fthinstanceoftheEuropeanJointConferencesonTheory and Practice of Software. ETAPS is an annual federated conference that was established in 1998 by combining a number of existing and new conferences. This year it comprised 5 conferences (FOSSACS, FASE, ESOP, CC, TACAS), 13 satellite workshops (ACL2, AGT, CMCS, COCV, DCC, INT, LDTA, SC, SFEDL, SLAP, SPIN, TPTS, and VISS), 8 invited lectures (not including those speci?c to the satellite events), and several tutorials. The events that comprise ETAPS address various aspects of the system - velopmentprocess,includingspeci?cation,design,implementation,analysis,and improvement. The languages, methodologies, and tools which support these - tivities are all well within its scope. Di?erent blends of theory and practice are represented, with an inclination towards theory with a practical motivation on one hand and soundly-based practice on the other. Many of the issues involved in software design apply to systems in general, including hardware systems, and the emphasis on software is not intended to be exclusive.