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Books in Numerical analysis

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Classical Recursion Theory, Volume II

  • 1st Edition
  • Volume 143
  • September 7, 1999
  • P. Odifreddi
  • English
  • Hardback
    9 7 8 - 0 - 4 4 4 - 5 0 2 0 5 - 6
Volume II of Classical Recursion Theory describes the universe from a local (bottom-upor synthetical) point of view, and covers the whole spectrum, from therecursive to the arithmetical sets.The first half of the book provides a detailed picture of the computablesets from the perspective of Theoretical Computer Science. Besides giving adetailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexityclasses, ranging from small time and space bounds to the elementary functions,with a particular attention to polynomial time and space computability. It alsodeals with primitive recursive functions and larger classes, which are ofinterest to the proof theorist. The second half of the book starts with the classical theory of recursivelyenumerable sets and degrees, which constitutes the core of Recursion orComputability Theory. Unlike other texts, usually confined to the Turingdegrees, the book covers a variety of other strong reducibilities, studyingboth their individual structures and their mutual relationships. The lastchapters extend the theory to limit sets and arithmetical sets. The volumeends with the first textbook treatment of the enumeration degrees, whichadmit a number of applications from algebra to the Lambda Calculus.The book is a valuable source of information for anyone interested inComplexity and Computability Theory. The student will appreciate the detailedbut informal account of a wide variety of basic topics, while the specialistwill find a wealth of material sketched in exercises and asides. A massivebibliography of more than a thousand titles completes the treatment on thehistorical side.

Computer Solution of Large Linear Systems

  • 1st Edition
  • Volume 28
  • June 16, 1999
  • Gerard Meurant
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 2 9 5 1 - 6
This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

Parallel Computational Fluid Dynamics '97

  • 1st Edition
  • April 1, 1998
  • D. Emerson + 4 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 3 8 3 7 - 2
Computational Fluid Dynamics (CFD) is a discipline that has always been in the vanguard of the exploitation of emerging and developing technologies. Advances in both algorithms and computers have rapidly been absorbed by the CFD community in its quest for more accurate simulations and reductions in the time to solution. Within this context, parallel computing has played an increasingly important role. Moreover, the uptake of parallel computing has brought the CFD community into ever-closer contact with hardware vendors and computer scientists. The multidisciplinary subject of parallel CFD and its rapidly evolving nature, in terms of hardware and software, requires a regular international meeting of this nature to keep abreast of the most recent developments.Parallel CFD '97 is part of an annual conference series dedicated to the discussion of recent developments and applications of parallel computing in the field of CFD and related disciplines. This was the 9th in the series, and since the inaugural conference in 1989, many new developments and technologies have emerged. The intervening years have also proved to be extremely volatile for many hardware vendors and a number of companies appeared and then disappeared. However, the belief that parallel computing is the only way forward has remained undiminished. Moreover, the increasing reliability and acceptance of parallel computers has seen many commercial companies now offering parallel versions of their codes, many developed within the EC funded EUROPORT activity, but generally for more modest numbers of processors. It is clear that industry has not moved to large scale parallel systems but it has shown a keen interest in more modest parallel systems recognising that parallel computing will play an important role in the future. This book forms the proceedings of the CFD '97 conference, which was organised by the the Computational Engineering Group at Daresbury Laboratory and held in Manchester, England, on May 19-21 1997. The sessions involved papers on many diverse subjects including turbulence, reactive flows, adaptive schemes, unsteady flows, unstructured mesh applications, industrial applications, developments in software tools and environments, climate modelling, parallel algorithms, evaluation of computer architectures and a special session devoted to parallel CFD at the AEREA research centres. This year's conference, like its predecessors, saw a continued improvement in both the quantity and quality of contributed papers.Since the conference series began many significant milestones have been acheived. For example in 1994, Massively Parallel Processing (MPP) became a reality with the advent of Cray T3D. This, of course, has brought with it the new challenge of scalability for both algorithms and architectures. In the 12 months since the 1996 conference, two more major milestones were achieved: microprocessors with a peak performance of a Gflop/s became available and the world's first Tflop/s calculation was performed. In the 1991 proceedings, the editors indicated that a Tflop/s computer was likely to be available in the latter half of this decade. On December 4th 1996, Intel achieved this breakthrough on the Linpack benchmark using 7,264 (200MHz) Pentium Pro microprocessors as part of the ASCI Red project. With the developments in MPP, the rapid rise of SMP architectures and advances in PC technology, the future for parallel CFD looks both promising and challenging.

Linear Algebra, Rational Approximation and Orthogonal Polynomials

  • 1st Edition
  • Volume 6
  • November 17, 1997
  • A. Bultheel + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 3 5 5 2 - 4
Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations.Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, and the lifting scheme for wavelet transform computation. The text serves as a supplement to existing books on structured linear algebra problems, rational approximation and orthogonal polynomials.Features of this book:• provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials• requires an elementary knowledge of calculus and linear algebra yet introduces advanced topics.The book will be of interest to applied mathematicians and engineers and to students and researchers.

Multiscale Wavelet Methods for Partial Differential Equations

  • 1st Edition
  • Volume 6
  • August 4, 1997
  • Wolfgang Dahmen + 2 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 3 7 1 4 - 6
This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource.

Analysis

  • 1st Edition
  • August 30, 1996
  • Ekkehard Kopp
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 2 8 7 2 - 2
Building on the basic concepts through a careful discussion of covalence, (while adhering resolutely to sequences where possible), the main part of the book concerns the central topics of continuity, differentiation and integration of real functions. Throughout, the historical context in which the subject was developed is highlighted and particular attention is paid to showing how precision allows us to refine our geometric intuition. The intention is to stimulate the reader to reflect on the underlying concepts and ideas.

Theory and Applications of Numerical Analysis

  • 2nd Edition
  • July 5, 1996
  • G. M. Phillips + 1 more
  • English
  • Paperback
    9 7 8 - 0 - 1 2 - 5 5 3 5 6 0 - 1
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 1 9 1 2 - 8
Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.

Numerical Methods for Partial Differential Equations

  • 3rd Edition
  • August 24, 1992
  • William F. Ames
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 7 1 3 0 - 0
This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation.

Scientific Computing and Differential Equations

  • 1st Edition
  • September 16, 1991
  • Gene H. Golub + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 1 6 6 9 - 1
Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context.This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level.