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Author : Josef Stoer,R. Bulirsch
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 50,5 Mb
Release : 2002-08-21
Category : Mathematics
ISBN : 9780387954523
New edition of a well-known classic in the field; Previous edition sold over 6000 copies worldwide; Fully-worked examples; Many carefully selected problems
Author : J. Stoer,R. Bulirsch
Publisher : Springer Science & Business Media
Page : 674 pages
File Size : 54,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722727
On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.
Author : Endre Süli,David F. Mayers
Publisher : Cambridge University Press
Page : 440 pages
File Size : 51,8 Mb
Release : 2003-08-28
Category : Mathematics
ISBN : 0521007941
An introduction to numerical analysis combining rigour with practical applications, and providing numerous exercises plus solutions.
Author : James F. Epperson
Publisher : John Wiley & Sons
Page : 614 pages
File Size : 51,6 Mb
Release : 2013-10-07
Category : Mathematics
ISBN : 9781118367599
Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."—Zentralblatt MATH ". . . carefully structured with many detailed worked examples."—The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB An appendix that contains proofs of various theorems and other material The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
Author : R.D Harding,D.A Quinney
Publisher : CRC Press
Page : 190 pages
File Size : 42,9 Mb
Release : 1989-01-01
Category : Mathematics
ISBN : 0852741545
Approximation techniques are widely used in mathematics and applied physics, as exact solutions are frequently impossible to obtain. A Simple Introduction to Numerical Analysis, Volume 2: Interpolation and Approximation extends the first volume to consider problems in interpolation and approximation. Topics covered include the construction of interpolating functions, the determination of polynomial and rational function approximations, numerical quadrature, and the solution of boundary value problems in ordinary differential equations. As with the previous volume, the text is integrated with a software package that allows the reader to work through numerous examples. It is also possible to use the software to consider problems that are beyond the scope of the text. The authors' expertise in combining text and software has resulted in a very readable work.
Author : Anonim
Publisher : Academic Publishers
Page : 312 pages
File Size : 42,9 Mb
Release : 2024-04-27
Category : Electronic
ISBN : 8187504676
Author : James F. Epperson
Publisher : John Wiley & Sons
Page : 526 pages
File Size : 40,7 Mb
Release : 2013-06-06
Category : Mathematics
ISBN : 9781118626238
Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math ". . . carefully structured with many detailed worked examples . . ." —The Mathematical Gazette ". . . an up-to-date and user-friendly account . . ." —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
Author : James F. Epperson
Publisher : John Wiley & Sons
Page : 277 pages
File Size : 45,7 Mb
Release : 2014-08-28
Category : Mathematics
ISBN : 9781118552131
A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB An appendix that contains proofs of various theorems and other material
Author : John Gregory,Don Redmond
Publisher : Jones & Bartlett Publishers
Page : 352 pages
File Size : 45,6 Mb
Release : 1994
Category : Mathematics
ISBN : UOM:39015032965322
Author : Kendall Atkinson
Publisher : John Wiley & Sons
Page : 726 pages
File Size : 44,5 Mb
Release : 1991-01-16
Category : Mathematics
ISBN : 9780471624899
This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New topics covered include optimization, trigonometric interpolation and the fast Fourier transform, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method, and the least squares solutions of systems of linear equations. Contains many problems, some with solutions.
Author : Robert M. Corless,Nicolas Fillion
Publisher : Springer Science & Business Media
Page : 869 pages
File Size : 46,9 Mb
Release : 2013-12-12
Category : Mathematics
ISBN : 9781461484530
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.
Author : Eugene E. Tyrtyshnikov
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681364
A logically organized advanced textbook, which turns the reader into an active participant by asking questions, hinting, giving direct recommendations, comparing different methods, and discussing "pessimistic" and "optimistic" approaches to numerical analysis. Advanced students and graduate students majoring in computer science, physics and mathematics will find this book helpful.
Author : A. Neumaier,Arnold Neumaier
Publisher : Cambridge University Press
Page : 368 pages
File Size : 55,8 Mb
Release : 2001-10
Category : Mathematics
ISBN : 0521336104
This textbook provides an introduction to constructive methods that provide accurate approximations to the solution of numerical problems using MATLAB.
Author : A. C. Faul
Publisher : CRC Press
Page : 292 pages
File Size : 46,7 Mb
Release : 2016-03-23
Category : Mathematics
ISBN : 9781498712194
This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is easily accessible, even to those with limited knowledge of mathematics. Students will get a concise, but thorough introduction to numerical analysis. In addition the algorithmic principles are emphasized to encourage a deeper understanding of why an algorithm is suitable, and sometimes unsuitable, for a particular problem. A Concise Introduction to Numerical Analysis strikes a balance between being mathematically comprehensive, but not overwhelming with mathematical detail. In some places where further detail was felt to be out of scope of the book, the reader is referred to further reading. The book uses MATLAB® implementations to demonstrate the workings of the method and thus MATLAB's own implementations are avoided, unless they are used as building blocks of an algorithm. In some cases the listings are printed in the book, but all are available online on the book’s page at www.crcpress.com. Most implementations are in the form of functions returning the outcome of the algorithm. Also, examples for the use of the functions are given. Exercises are included in line with the text where appropriate, and each chapter ends with a selection of revision exercises. Solutions to odd-numbered exercises are also provided on the book’s page at www.crcpress.com. This textbook is also an ideal resource for graduate students coming from other subjects who will use numerical techniques extensively in their graduate studies.
Author : Timo Heister,Leo G. Rebholz,Fei Xue
Publisher : Walter de Gruyter GmbH & Co KG
Page : 193 pages
File Size : 46,5 Mb
Release : 2019-03-18
Category : Mathematics
ISBN : 9783110573336
Numerical analysis deals with the development and analysis of algorithms for scientific computing, and is in itself a very important part of mathematics, which has become more and more prevalent across the mathematical spectrum. This book is an introduction to numerical methods for solving linear and nonlinear systems of equations as well as ordinary and partial differential equations, and for approximating curves, functions, and integrals.