Accuracy And Stability Of Numerical Algorithms

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Accuracy and Stability of Numerical Algorithms

Nicholas J. Higham
Accuracy and Stability of Numerical Algorithms Book PDF

Author : Nicholas J. Higham
Publisher : SIAM
Page : 710 pages
File Size : 41,7 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0898718023

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Accuracy and Stability of Numerical Algorithms by Nicholas J. Higham Pdf

Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

Accuracy and Stability of Numerical Algorithms

Nicholas J. Higham
Accuracy and Stability of Numerical Algorithms Book PDF

Author : Nicholas J. Higham
Publisher : SIAM
Page : 690 pages
File Size : 40,9 Mb
Release : 2002-08-01
Category : Mathematics
ISBN : 9780898715217

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Accuracy and Stability of Numerical Algorithms by Nicholas J. Higham Pdf

Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

Numerical Algorithms

Justin Solomon
Numerical Algorithms Book PDF

Author : Justin Solomon
Publisher : CRC Press
Page : 400 pages
File Size : 50,6 Mb
Release : 2015-06-24
Category : Computers
ISBN : 9781482251890

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Numerical Algorithms by Justin Solomon Pdf

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

MATLAB Guide, Third Edition

Desmond J. Higham,Nicholas J. Higham
MATLAB Guide Third Edition Book PDF

Author : Desmond J. Higham,Nicholas J. Higham
Publisher : SIAM
Page : 485 pages
File Size : 46,7 Mb
Release : 2016-12-27
Category : Science
ISBN : 9781611974652

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MATLAB Guide, Third Edition by Desmond J. Higham,Nicholas J. Higham Pdf

MATLAB is an interactive system for numerical computation that is widely used for teaching and research in industry and academia. It provides a modern programming language and problem solving environment, with powerful data structures, customizable graphics, and easy-to-use editing and debugging tools. This third edition of MATLAB Guide completely revises and updates the best-selling second edition and is more than 30 percent longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox. Key features are a tutorial in Chapter 1 that gives a hands-on overview of MATLAB; a thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers; and a web page at http://www.siam.org/books/ot150 that provides example program files, updates, and links to MATLAB resources. The new edition contains color figures throughout; includes pithy discussions of related topics in new ?Asides" boxes that augment the text; has new chapters on the Parallel Computing Toolbox, object-oriented programming, graphs, and large data sets; covers important new MATLAB data types such as categorical arrays, string arrays, tall arrays, tables, and timetables; contains more on MATLAB workflow, including the Live Editor and unit tests; and fully reflects major updates to the MATLAB graphics system. This book is suitable for both beginners and more experienced users, including students, researchers, and practitioners.

Numerical Analysis with Algorithms and Programming

Santanu Saha Ray
Numerical Analysis with Algorithms and Programming Book PDF

Author : Santanu Saha Ray
Publisher : CRC Press
Page : 391 pages
File Size : 41,9 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781498741835

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Numerical Analysis with Algorithms and Programming by Santanu Saha Ray Pdf

Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization Approximation of functions and least square approximation Numerical differentiation and divided differences Numerical quadrature and integration Numerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs) The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.

The Concept of Stability in Numerical Mathematics

Wolfgang Hackbusch
The Concept of Stability in Numerical Mathematics Book PDF

Author : Wolfgang Hackbusch
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 54,8 Mb
Release : 2014-02-06
Category : Mathematics
ISBN : 9783642393860

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The Concept of Stability in Numerical Mathematics by Wolfgang Hackbusch Pdf

In this book, the author compares the meaning of stability in different subfields of numerical mathematics. Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.

Numerical Analysis of Spectral Methods

David Gottlieb,Steven A. Orszag
Numerical Analysis of Spectral Methods Book PDF

Author : David Gottlieb,Steven A. Orszag
Publisher : SIAM
Page : 167 pages
File Size : 55,9 Mb
Release : 1977-01-01
Category : Technology & Engineering
ISBN : 9780898710236

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Numerical Analysis of Spectral Methods by David Gottlieb,Steven A. Orszag Pdf

A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.

A Graduate Introduction to Numerical Methods

Robert M. Corless,Nicolas Fillion
A Graduate Introduction to Numerical Methods Book PDF

Author : Robert M. Corless,Nicolas Fillion
Publisher : Springer Science & Business Media
Page : 869 pages
File Size : 46,8 Mb
Release : 2013-12-12
Category : Mathematics
ISBN : 9781461484530

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A Graduate Introduction to Numerical Methods by Robert M. Corless,Nicolas Fillion Pdf

This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

Numerical Matrix Analysis

Ilse C. F. Ipsen
Numerical Matrix Analysis Book PDF

Author : Ilse C. F. Ipsen
Publisher : SIAM
Page : 135 pages
File Size : 40,9 Mb
Release : 2009-07-23
Category : Mathematics
ISBN : 9780898716764

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Numerical Matrix Analysis by Ilse C. F. Ipsen Pdf

Matrix analysis presented in the context of numerical computation at a basic level.

A First Course in Numerical Methods

Uri M. Ascher,Chen Greif
A First Course in Numerical Methods Book PDF

Author : Uri M. Ascher,Chen Greif
Publisher : SIAM
Page : 574 pages
File Size : 45,8 Mb
Release : 2011-07-14
Category : Mathematics
ISBN : 9780898719970

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A First Course in Numerical Methods by Uri M. Ascher,Chen Greif Pdf

Offers students a practical knowledge of modern techniques in scientific computing.

Numerical Methods for Conservation Laws

Jan S. Hesthaven
Numerical Methods for Conservation Laws Book PDF

Author : Jan S. Hesthaven
Publisher : SIAM
Page : 570 pages
File Size : 48,7 Mb
Release : 2018-01-30
Category : Science
ISBN : 9781611975109

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Numerical Methods for Conservation Laws by Jan S. Hesthaven Pdf

Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication.

An Introduction to Numerical Analysis

Endre Süli,David F. Mayers
An Introduction to Numerical Analysis Book PDF

Author : Endre Süli,David F. Mayers
Publisher : Cambridge University Press
Page : 440 pages
File Size : 55,8 Mb
Release : 2003-08-28
Category : Mathematics
ISBN : 0521007941

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An Introduction to Numerical Analysis by Endre Süli,David F. Mayers Pdf

An introduction to numerical analysis combining rigour with practical applications, and providing numerous exercises plus solutions.

Numerical Methods in Matrix Computations

Åke Björck
Numerical Methods in Matrix Computations Book PDF

Author : Åke Björck
Publisher : Springer
Page : 800 pages
File Size : 46,9 Mb
Release : 2014-10-07
Category : Mathematics
ISBN : 9783319050898

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Numerical Methods in Matrix Computations by Åke Björck Pdf

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Modeling of Atmospheric Chemistry

Guy P. Brasseur,Daniel J. Jacob
Modeling of Atmospheric Chemistry Book PDF

Author : Guy P. Brasseur,Daniel J. Jacob
Publisher : Cambridge University Press
Page : 632 pages
File Size : 51,7 Mb
Release : 2017-05-04
Category : Science
ISBN : 9781108216357

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Modeling of Atmospheric Chemistry by Guy P. Brasseur,Daniel J. Jacob Pdf

Mathematical modeling of atmospheric composition is a formidable scientific and computational challenge. This comprehensive presentation of the modeling methods used in atmospheric chemistry focuses on both theory and practice, from the fundamental principles behind models, through to their applications in interpreting observations. An encyclopaedic coverage of methods used in atmospheric modeling, including their advantages and disadvantages, makes this a one-stop resource with a large scope. Particular emphasis is given to the mathematical formulation of chemical, radiative, and aerosol processes; advection and turbulent transport; emission and deposition processes; as well as major chapters on model evaluation and inverse modeling. The modeling of atmospheric chemistry is an intrinsically interdisciplinary endeavour, bringing together meteorology, radiative transfer, physical chemistry and biogeochemistry, making the book of value to a broad readership. Introductory chapters and a review of the relevant mathematics make this book instantly accessible to graduate students and researchers in the atmospheric sciences.

Handbook for Automatic Computation

John H. Wilkinson,C. Reinsch
Handbook for Automatic Computation Book PDF

Author : John H. Wilkinson,C. Reinsch
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642869402

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Handbook for Automatic Computation by John H. Wilkinson,C. Reinsch Pdf

The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment.