Computer Solution of Large Linear Systems

Author: Gerard Meurant

Publisher: Elsevier

ISBN: 9780080529516

Category: Mathematics

Page: 776

View: 7567

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.

Numerische Mathematik 1

Eine Einführung — unter Berücksichtigung von Vorlesungen von F. L. Bauer

Author: Josef Stoer

Publisher: Springer-Verlag

ISBN: 3662090236

Category: Mathematics

Page: 371

View: 7638

Aus den Besprechungen: "Diese Einführung zeichnet sich durch eine klare, gut lesbare Darstellung aus und ist eine gelungene Synthese zwischen theoretischer Begründung und praktischer Anwendung der behandelten Methoden. Deshalb ist sie auch zu einem Standardlehrbuch der Numerischen Mathematik geworden." #Internationale Mathematische Nachrichten#1 "Unter den Numerik-Lehrbüchern ... sei auf das vorliegende Buch besonders hingewiesen, da hier bei allen Ansprüchen an mathematische Strenge das Schwergewicht auf die Bereitstellung von praktikablen Algorithmen nach neuesten Erkenntnissen mit vielen numerischen Beispielen und kritischen Beurteilungen liegt..." #Die neue Hochschule#

Numerical Methods for Bifurcation Problems

Proceedings of the Conference at the University of Dortmund, August 22–26, 1983


Publisher: Springer-Verlag

ISBN: 3034862563

Category: Juvenile Nonfiction

Page: 584

View: 4007

Laser Spectroscopy IV

Proceedings of the Fourth International Conference, Rottarch-Egern, Fed. Rep. of Germany, June 11-15, 1979

Author: David Padua

Publisher: Springer Science & Business Media

ISBN: 038709766X

Category: Computers

Page: 2175

View: 9665

Traditionally, the discipline of parallel computing has encompassed a wide range of topics ranging from machine organization all the way to applications. The Encyclopedia of Parallel Computing is likewise broad in scope, covering machine organization, programming, algorithms, and applications. Within each area, the Encyclopedia covers concepts, designs, and specific implementations. In the area of algorithms, the encyclopedia will cover (1) concepts such as cache-oblivious algorithms and systolic algorithms, (2) specific numerical and non-numerical algorithms such as parallel matrix-matrix multiplication and graph algorithms to, for example, find connected components in parallel, and (3) implementations of algorithms in the form of widely used libraries such as LAPACK. In the area of architecture, the encyclopedia will contain (1) concepts such as sequential consistency and cache coherency, (2) machine classes such as shared-memory multiprocessors and dataflow machines, and (3) specific machines such as IBM's cell processor and Intel's multicore machines. In the area of software, it will cover (1) concepts such as races and autoparallelization, and (2) designs in the form of parallel programming languages, library interfaces, and operating systems. The encyclopedia also will cover application issues emphasizing the type of parallel computation involved and the magnitude in terms of computational requirements of the applications.Each encyclopedia entry will be concise and clear and will contain references to the literature for readers wishing to study the topic of the entry in depth. The broad coverage--together with extensive pointers to the literature for in-depth study'will make the encyclopedia an invaluable reference tool for researchers, practitioners and students alike.

Adjustment Computations

Spatial Data Analysis

Author: Charles D. Ghilani

Publisher: John Wiley & Sons

ISBN: 1118174402

Category: Technology & Engineering

Page: 672

View: 5145

the complete guide to adjusting for measurement error—expanded and updated no measurement is ever exact. Adjustment Computations updates a classic, definitive text on surveying with the latest methodologies and tools for analyzing and adjusting errors with a focus on least squares adjustments, the most rigorous methodology available and the one on which accuracy standards for surveys are based. This extensively updated Fifth Edition shares new information on advances in modern software and GNSS-acquired data. Expanded sections offer a greater amount of computable problems and their worked solutions, while new screenshots guide readers through the exercises. Continuing its legacy as a reliable primer, Adjustment Computations covers the basic terms and fundamentals of errors and methods of analyzing them and progresses to specific adjustment computations and spatial information analysis. Current and comprehensive, the book features: Easy-to-understand language and an emphasis on real-world applications Analyzing data in three dimensions, confidence intervals, statistical testing, and more An updated support web page containing a 150-page solutions manual, software (STATS, ADJUST, and MATRIX for Windows computers), MathCAD worksheets, and more at The latest information on advanced topics such as the tau criterion used in post-adjustment statistical blunder detection Adjustment Computations, Fifth Edition is an invaluable reference and self-study resource for working surveyors, photogrammetrists, and professionals who use GNSS and GIS for data collection and analysis, including oceanographers, urban planners, foresters, geographers, and transportation planners. It's also an indispensable resource for students preparing for licensing exams and the ideal textbook for courses in surveying, civil engineering, forestry, cartography, and geology.

Iterative Solution of Large Sparse Systems of Equations

Author: Wolfgang Hackbusch

Publisher: Springer

ISBN: 3319284835

Category: Mathematics

Page: 509

View: 5215

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.

Applied Parallel Computing

State of the Art in Scientific Computing

Author: Jack Dongarra,Kaj Madsen

Publisher: Springer Science & Business Media

ISBN: 3540290672

Category: Computers

Page: 1174

View: 4671

Introduction The PARA workshops in the past were devoted to parallel computing methods in science and technology. There have been seven PARA meetings to date: PARA’94, PARA’95 and PARA’96 in Lyngby, Denmark, PARA’98 in Umea, ? Sweden, PARA 2000 in Bergen, N- way, PARA 2002 in Espoo, Finland, and PARA 2004 again in Lyngby, Denmark. The ?rst six meetings featured lectures in modern numerical algorithms, computer science, en- neering, and industrial applications, all in the context of scienti?c parallel computing. This meeting in the series, the PARA 2004 Workshop with the title “State of the Art in Scienti?c Computing”, was held in Lyngby, Denmark, June 20–23, 2004. The PARA 2004 Workshop was organized by Jack Dongarra from the University of Tennessee and Oak Ridge National Laboratory, and Kaj Madsen and Jerzy Was ́niewski from the Technical University of Denmark. The emphasis here was shifted to high-performance computing (HPC). The ongoing development of ever more advanced computers provides the potential for solving increasingly dif?cult computational problems. However, given the complexity of modern computer architectures, the task of realizing this potential needs careful attention. For example, the failure to exploit a computer’s memory hi- archy can degrade performance badly. A main concern of HPC is the development of software that optimizes the performance of a given computer. The high cost of state-of-the-art computers can be prohibitive for many workplaces, especially if there is only an occasional need for HPC.

Hierarchische Matrizen

Algorithmen und Analysis

Author: Wolfgang Hackbusch

Publisher: Springer Science & Business Media

ISBN: 3642002218

Category: Mathematics

Page: 451

View: 3955

Bei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große, eventuell auch voll besetzte Matrizen. In dem Band stellt der Autor eine neuartige Methode dar, die es erstmals erlaubt, solche Matrizen nicht nur effizient zu speichern, sondern auch alle Matrixoperationen einschließlich der Matrixinversion bzw. der Dreieckszerlegung approximativ durchzuführen. Anwendung findet diese Technik nicht nur bei der Lösung großer Gleichungssysteme, sondern auch bei Matrixgleichungen und der Berechnung von Matrixfunktionen.

Numerical Linear Algebra with Applications


Author: William Ford

Publisher: Academic Press

ISBN: 0123947847

Category: Mathematics

Page: 628

View: 7835

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

Proceedings of the 2011 2nd International Congress on Computer Applications and Computational Science

Author: Ford Lumban Gaol,Quang Vinh Nguyen

Publisher: Springer Science & Business Media

ISBN: 364228308X

Category: Computers

Page: 516

View: 6764

The latest inventions in computer technology influence most of human daily activities. In the near future, there is tendency that all of aspect of human life will be dependent on computer applications. In manufacturing, robotics and automation have become vital for high quality products. In education, the model of teaching and learning is focusing more on electronic media than traditional ones. Issues related to energy savings and environment is becoming critical. Computational Science should enhance the quality of human life, not only solve their problems. Computational Science should help humans to make wise decisions by presenting choices and their possible consequences. Computational Science should help us make sense of observations, understand natural language, plan and reason with extensive background knowledge. Intelligence with wisdom is perhaps an ultimate goal for human-oriented science. This book is a compilation of some recent research findings in computer application and computational science. This book provides state-of-the-art accounts in Computer Control and Robotics, Computers in Education and Learning Technologies, Computer Networks and Data Communications, Data Mining and Data Engineering, Energy and Power Systems, Intelligent Systems and Autonomous Agents, Internet and Web Systems, Scientific Computing and Modeling, Signal, Image and Multimedia Processing, and Software Engineering.

Algorithms for Parallel Processing

Author: Michael T. Heath,Abhiram Ranade,Robert S. Schreiber

Publisher: Springer Science & Business Media

ISBN: 9780387986807

Category: Mathematics

Page: 373

View: 7464

This IMA Volume in Mathematics and its Applications ALGORITHMS FOR PARALLEL PROCESSING is based on the proceedings of a workshop that was an integral part of the 1996-97 IMA program on "MATHEMATICS IN HIGH-PERFORMANCE COMPUTING. " The workshop brought together algorithm developers from theory, combinatorics, and scientific computing. The topics ranged over models, linear algebra, sorting, randomization, and graph algorithms and their analysis. We thank Michael T. Heath of University of lllinois at Urbana (Com puter Science), Abhiram Ranade of the Indian Institute of Technology (Computer Science and Engineering), and Robert S. Schreiber of Hewlett Packard Laboratories for their excellent work in organizing the workshop and editing the proceedings. We also take this opportunity to thank the National Science Founda tion (NSF) and the Army Research Office (ARO), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The Workshop on Algorithms for Parallel Processing was held at the IMA September 16 - 20, 1996; it was the first workshop of the IMA year dedicated to the mathematics of high performance computing. The work shop organizers were Abhiram Ranade of The Indian Institute of Tech nology, Bombay, Michael Heath of the University of Illinois, and Robert Schreiber of Hewlett Packard Laboratories. Our idea was to bring together researchers who do innovative, exciting, parallel algorithms research on a wide range of topics, and by sharing insights, problems, tools, and methods to learn something of value from one another.

High Performance Computing for Computational Science - VECPAR 2004

6th International Conference, Valencia, Spain, June 28-30, 2004, Revised Selected and Invited Papers

Author: Michel Daydé,Jack Dongarra,Vincente Hernández,José M.L.M. Palma

Publisher: Springer Science & Business Media

ISBN: 9783540254249

Category: Computers

Page: 732

View: 5194

This book constitutes the thoroughly refereed post-proceedings of the 6th International Conference on High Performance Computing for Computational Science, VECPAR 2004, held in Valencia, Spain, in June 2004. The 48 revised full papers presented together with 5 invited papers were carefully selected during two rounds of reviewing and improvement from initially 130 contributions. The papers are organized in topical sections on large-scale computations, data management and data mining, GRID computing infrastructure, cluster computing, parallel and distributed computing, and computational linear and non-linear algebra.

Programming Finite Elements in JavaTM

Author: Gennadiy P. Nikishkov

Publisher: Springer Science & Business Media

ISBN: 9781848829725

Category: Technology & Engineering

Page: 402

View: 1399

Programming Finite Elements in JavaTM teaches the reader how to programme the algorithms of the finite element method (FEM) in JavaTM. The compact, simple code helps the student to read the algorithms, to understand them and thus to be able to refine them. All of the main aspects of finite element techniques are considered: finite element solution; generation of finite element meshes; and visualization of finite element models and results with Java 3DTM. The step-by-step presentation includes algorithm programming and code explanation at each point. Problems and exercises are provided for each chapter, with JavaTM source code and problem data sets available from

Finite Element Solution of Boundary Value Problems

Theory and Computation

Author: O. Axelsson,V. A. Barker

Publisher: Academic Press

ISBN: 1483260569

Category: Mathematics

Page: 452

View: 3357

Finite Element Solution of Boundary Value Problems: Theory and Computation provides an introduction to both the theoretical and computational aspects of the finite element method for solving boundary value problems for partial differential equations. This book is composed of seven chapters and begins with surveys of the two kinds of preconditioning techniques, one based on the symmetric successive overrelaxation iterative method for solving a system of equations and a form of incomplete factorization. The subsequent chapters deal with the concepts from functional analysis of boundary value problems. These topics are followed by discussions of the Ritz method, which minimizes the quadratic functional associated with a given boundary value problem over some finite-dimensional subspace of the original space of functions. Other chapters are devoted to direct methods, including Gaussian elimination and related methods, for solving a system of linear algebraic equations. The final chapter continues the analysis of preconditioned conjugate gradient methods, concentrating on applications to finite element problems. This chapter also looks into the techniques for reducing rounding errors in the iterative solution of finite element equations. This book will be of value to advanced undergraduates and graduates in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined workers in engineering and the physical sciences.

Numerical Solution of Systems of Nonlinear Algebraic Equations

Author: George D. Byrne,Charles A. Hall

Publisher: Elsevier

ISBN: 1483269302

Category: Mathematics

Page: 430

View: 1708

Numerical Solution of Systems of Nonlinear Algebraic Equations contains invited lectures of the NSF-CBMS Regional Conference on the Numerical Solution of Nonlinear Algebraic Systems with Applications to Problems in Physics, Engineering and Economics, held on July 10-14, 1972. This book is composed of 10 chapters and begins with the concepts of nonlinear algebraic equations in continuum mechanics. The succeeding chapters deal with the numerical solution of quasilinear elliptic equations, the nonlinear systems in semi-infinite programming, and the solution of large systems of linear algebraic equations. These topics are followed by a survey of some computational techniques for the nonlinear least squares problem. The remaining chapters explore the problem of nonlinear functional minimization, the modification methods, and the computer-oriented algorithms for solving system. These chapters also examine the principles of contractor theory of solving equations. This book will prove useful to undergraduate and graduate students.