Matrix Preconditioning Techniques And Applications

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Author : Edward A. Hirsch
ISBN : 9783540797098
Genre : Computers
File Size : 56.75 MB
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This book constitutes the refereed proceedings of the Third International Computer Science Symposium in Russia, CSR 2008, held in Moscow, Russia, June 7-12, 2008. The 33 revised papers presented together with 5 invited papers and one opening lecture were carefully reviewed and selected from 103 submissions. All major areas in computer science are addressed. The theory track deals with algorithms, protocols, and data structures; complexity and cryptography; formal languages, automata and their applications to computer science; computational models and concepts; proof theory and applications of logic to computer science. The application part comprises programming and languages; computer architecture and hardware design; symbolic computing and numerical applications; application software; artificial intelligence and robotics.

Author : Ivan Dimov
ISBN : 9783540006084
Genre : Computers
File Size : 80.57 MB
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Nuclear magnetic resonance spectroscopy is one of the most important analytical methods available today. This practice-oriented textbook aims at teaching the use of NMR spectra in the elucidation of organic structures. The emphasis of NMR - from Spectra to Structures is on practical rather than on theoretical aspects, which are treated only briefly. The book is intended as a practical guide to today's standard NMR experiments for students and laboratory personnel. A set of thirty-five graded problems reinforces the reader's understanding of how problems of structure elucidation are solved by using NMR.

Author : Iman Farahbakhsh
ISBN : 9781119618706
Genre : Science
File Size : 80.58 MB
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A succinct and complete explanation of Krylov subspace methods for solving matrices Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers is the most current and complete guide to the implementation of Krylov subspace methods for solving systems of equations with different types of matrices. Written in the simplest language possible and eliminating ambiguities, the text is easy to follow for post-grad students and applied mathematicians alike. The book covers a breadth of topics, including: The different methods used in solving the systems of equations with ill-conditioned and well-conditioned matrices. The behavior of Krylov subspace methods in the solution of systems with ill-posed singular matrices The book includes executable subroutines and main programs that can be applied in CFD codes as well as appendices that support the results provided throughout the text. There is no other comparable resource to prepare the reader to use Krylov subspace methods in incompressible fluid flow solvers.

Author : William Ford
ISBN : 9780123947840
Genre : Mathematics
File Size : 23.46 MB
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Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra Detailed explanations and examples A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra Examples from engineering and science applications

Author : Elias A. Lipitakis
ISBN : 9810212925
Genre : Computers
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This volume contains selected papers of the proceedings of the first Hellenic Conference on Mathematics and Informatics (HERMIS '92). The main theme for HERMIS '92 Conference was Computer Mathematics, with special emphasis on Computational Mathematics, Operational Research and Statistics, and Mathematics in Economic Science. The presented papers of the HERMIS Conference have been classified into the following technical sessions: Numerical solution of Differential Equations, Parallel Processing and Parallel Algorithms, Optimization and Approximation, Algorithms in Operational Research and Control Theory, Statistical Methods and Analysis, Mathematics in Economic Science, Artificial Intelligence and Data Bases Technology.In addition, a number of selected research articles published recently in the Hellenic Mathematical Society Bulletin in the form of special issues on Computer Mathematics (Volumes 31 and 32) are also included.

Author : Maxim A. Olshanskii
ISBN : 9781611973464
Genre : Mathematics
File Size : 62.39 MB
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Iterative Methods for Linear Systems÷offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.÷÷

Author : Are Magnus Bruaset
ISBN : 0582276543
Genre : Mathematics
File Size : 70.86 MB
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The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are well suited for the kind of systems arising from the discretization of partial differential equations. The focus of this presentation is on the family of Krylov subspace solvers, of which the Conjugate Gradient algorithm is a typical example. In addition to an introduction to the basic principles of such methods, a large number of specific algorithms for symmetric and nonsymmetric problems are discussed. When solving linear systems by iteration, a preconditioner is usually introduced in order to speed up convergence. In many cases, the selection of a proper preconditioner is crucial to the resulting computational performance. For this reason, this book pays special attention to different preconditioning strategies. Although aimed at a wide audience, the presentation assumes that the reader has basic knowledge of linear algebra, and to some extent, of partial differential equations. The comprehensive bibliography in this survey is provides an entry point to the enormous amount of published research in the field of iterative methods.

Author : Dario Andrea Bini
ISBN : 3764389966
Genre : Mathematics
File Size : 77.42 MB
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This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.

Author : Heinrich Freistühler
ISBN : 3764367105
Genre : Mathematics
File Size : 83.19 MB
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Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.

An undergraduate textbook that highlights motivating applications and contains summary sections, examples, exercises, online MATLAB codes and a MATLAB toolkit. All the major topics of computational linear algebra are covered, from basic concepts to advanced topics such as the quadratic eigenvalue problem in later chapters.

Author : Charles George Broyden
ISBN : 0080478875
Genre : Mathematics
File Size : 26.57 MB
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The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of the block conjugate-gradient algorithm and it is this observation that permits the unification of the theory. The two major sub-classes of those methods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as natural generalisations of the Orthodir (GCR) and Orthomin algorithms. These are themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt algorithm and their properties, in particular their stability properties, are determined by the two matrices that define the block conjugate-gradient algorithm. These are the matrix of coefficients and the preconditioning matrix. In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms. In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM. Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices. · comprehensive and unified approach · up-to-date chapter on preconditioners · complete theory of stability · includes dual and reverse methods · comparison of algorithms on CD-ROM · objective assessment of algorithms