logo资料库

Numerical Analysis (2nd edition, Walter Gautschi).pdf

发布时间：2022-06-02 发布人：admin 分类：说明书 资料大小：5.59M 资料格式：pdf 举报 版权申诉
第1页 / 共611页
第2页 / 共611页
第3页 / 共611页
第4页 / 共611页
第5页 / 共611页
第6页 / 共611页
第7页 / 共611页
第8页 / 共611页
资料共611页，剩余部分请下载后查看
    GetFullPageImage
    front-matter
    Numerical Analysis
    Preface to the Second Edition
    Preface to the First Edition
    Contents
    Prologue
    P1 Overview
    P2 Numerical Analysis Software
    P3 Textbooks and Monographs
    P3.1 Selected Textbooks on Numerical Analysis
    P3.2 Monographs and Books on Specialized Topics
    P4 Journals
    fulltext
    Chapter 1: Machine Arithmetic and Related Matters
    1.1 Real Numbers, Machine Numbers, and Rounding
    1.1.1 Real Numbers
    1.1.2 Machine Numbers
    1.1.2.1 Floating-Point Numbers
    1.1.2.2 Fixed-Point Numbers
    1.1.2.3 Other Data Structures for Numbers
    1.1.3 Rounding
    1.2 Machine Arithmetic
    1.2.1 A Model of Machine Arithmetic
    1.2.2 Error Propagation in Arithmetic Operations:Cancellation Error
    1.3 The Condition of a Problem
    1.3.1 Condition Numbers
    1.3.2 Examples
    1.4 The Condition of an Algorithm
    1.5 Computer Solution of a Problem; Overall Error
    1.6 Notes to Chapter 1
    Exercises and Machine Assignments to Chapter 1
    Exercises
    Machine Assignments
    Selected Solutions to Exercises
    Selected Solutions to Machine Assignments
    fulltext(1)
    Chapter 2: Approximation and Interpolation
    2.1 Least Squares Approximation
    2.1.1 Inner Products
    2.1.2 The Normal Equations
    2.1.3 Least Squares Error; Convergence
    2.1.4 Examples of Orthogonal Systems
    2.2 Polynomial Interpolation
    2.2.1 Lagrange Interpolation Formula: Interpolation Operator
    2.2.2 Interpolation Error
    2.2.3 Convergence
    2.2.4 Chebyshev Polynomials and Nodes
    2.2.5 Barycentric Formula
    2.2.6 Newton's Formula
    2.2.7 Hermite Interpolation
    2.2.8 Inverse Interpolation
    2.3 Approximation and Interpolation by Spline Functions
    2.3.1 Interpolation by Piecewise Linear Functions
    2.3.2 A Basis for S10 (Δ )
    2.3.3 Least Squares Approximation
    2.3.4 Interpolation by Cubic Splines
    2.3.5 Minimality Properties of Cubic Spline Interpolants
    2.4 Notes to Chapter 2
    Exercises and Machine Assignments to Chapter 2
    Exercises
    Machine Assignments
    Selected Solutions to Exercises
    Selected Solutions to Machine Assignments
    fulltext(2)
    Chapter 3: Numerical Differentiation and Integration
    3.1 Numerical Differentiation
    3.1.1 A General Differentiation Formula for Unequally Spaced Points
    3.1.2 Examples
    3.1.3 Numerical Differentiation with Perturbed Data
    3.2 Numerical Integration
    3.2.1 The Composite Trapezoidal and Simpson's Rules
    3.2.2 (Weighted) Newton–Cotes and Gauss Formulae
    3.2.3 Properties of Gaussian Quadrature Rules
    3.2.4 Some Applications of the Gauss Quadrature Rule
    3.2.5 Approximation of Linear Functionals: Methodof Interpolation vs. Method of UndeterminedCoefficients
    3.2.6 Peano Representation of Linear Functionals
    3.2.7 Extrapolation Methods
    3.3 Notes to Chapter 3
    Exercises and Machine Assignments to Chapter 3
    Exercises
    Machine Assignments
    Selected Solutions to Exercises
    Selected Solutions to Machine Assignments
    fulltext(3)
    Chapter 4: Nonlinear Equations
    4.1 Examples
    4.1.1 A Transcendental Equation
    4.1.2 A Two-Point Boundary Value Problem
    4.1.3 A Nonlinear Integral Equation
    4.1.4 s-Orthogonal Polynomials
    4.2 Iteration, Convergence, and Efficiency
    4.3 The Methods of Bisection and Sturm Sequences
    4.3.1 Bisection Method
    4.3.2 Method of Sturm Sequences
    4.4 Method of False Position
    4.5 Secant Method
    4.6 Newton's Method
    4.7 Fixed Point Iteration
    4.8 Algebraic Equations
    4.8.1 Newton's Method Applied to an Algebraic Equation
    4.8.2 An Accelerated Newton Method for Equations with Real Roots
    4.9 Systems of Nonlinear Equations
    4.9.1 Contraction Mapping Principle
    4.9.2 Newton's Method for Systems of Equations
    4.10 Notes to Chapter 4
    Exercises and Machine Assignments to Chapter 4
    Exercises
    Machine Assignments
    Selected Solutions to Exercises
    Selected Solutions to Machine Assignments
    fulltext(4)
    Chapter 5: Initial Value Problems for ODEs: One-Step Methods
    5.1 Examples
    5.2 Types of Differential Equations
    5.3 Existence and Uniqueness
    5.4 Numerical Methods
    5.5 Local Description of One-Step Methods
    5.6 Examples of One-Step Methods
    5.6.1 Euler's Method
    5.6.2 Method of Taylor Expansion
    5.6.3 Improved Euler Methods
    5.6.4 Second-Order Two-Stage Methods
    5.6.5 Runge–Kutta Methods
    5.7 Global Description of One-Step Methods
    5.7.1 Stability
    5.7.2 Convergence
    5.7.3 Asymptotics of Global Error
    5.8 Error Monitoring and Step Control
    5.8.1 Estimation of Global Error
    5.8.2 Truncation Error Estimates
    5.8.3 Step Control
    5.9 Stiff Problems
    5.9.1 A-Stability
    5.9.2 Padé Approximation
    5.9.3 Examples of A-Stable One-Step Methods
    5.9.4 Regions of Absolute Stability
    5.10 Notes to Chapter 5
    Exercises and Machine Assignments to Chapter 5
    Exercises
    Machine Assignments
    Selected Solutions to Exercises
    Selected Solutions to Machine Assignments
    fulltext(5)
    Chapter 6: Initial Value Problems for ODEs: Multistep Methods
    6.1 Local Description of Multistep Methods
    6.1.1 Explicit and Implicit Methods
    6.1.2 Local Accuracy
    6.1.3 Polynomial Degree vs. Order
    6.2 Examples of Multistep Methods
    6.2.1 Adams–Bashforth Method
    6.2.2 Adams–Moulton Method
    6.2.3 Predictor–Corrector Methods
    6.3 Global Description of Multistep Methods
    6.3.1 Linear Difference Equations
    6.3.1.1 Homogeneous Equation
    6.3.1.2 Inhomogeneous Equation
    6.3.2 Stability and Root Condition
    6.3.3 Convergence
    6.3.4 Asymptotics of Global Error
    6.3.5 Estimation of Global Error
    6.4 Analytic Theory of Order and Stability
    6.4.1 Analytic Characterization of Order
    6.4.2 Stable Methods of Maximum Order
    6.4.3 Applications
    6.5 Stiff Problems
    6.5.1 A-Stability
    6.5.2 A(α)-Stability
    6.6 Notes to Chapter 6
    Exercises and Machine Assignments to Chapter 6
    Exercises
    Machine Assignments
    Selected Solutions to Exercises
    Selected Solutions to Machine Assignments
    fulltext(6)
    Chapter 7: Two-Point Boundary Value Problems for ODEs
    7.1 Existence and Uniqueness
    7.1.1 Examples
    7.1.2 A Scalar Boundary Value Problem
    7.1.3 General Linear and Nonlinear Systems
    7.2 Initial Value Techniques
    7.2.1 Shooting Method for a Scalar Boundary Value Problem
    7.2.2 Linear and Nonlinear Systems
    7.2.3 Parallel Shooting
    7.3 Finite Difference Methods
    7.3.1 Linear Second-Order Equations
    7.3.2 Nonlinear Second-Order Equations
    7.4 Variational Methods
    7.4.1 Variational Formulation
    7.4.2 The Extremal Problem
    7.4.3 Approximate Solution of the Extremal Problem
    7.5 Notes to Chapter7
    Exercises and Machine Assignments to Chapter 7
    Exercises
    Machine Assignments
    Selected Solutions to Exercises
    Selected Solutions to Machine Assignments
    back-matter
    References
    Index
    Walter Gautschi Numerical Analysis Second Edition
    Walter Gautschi Department of Computer Sciences Purdue University 250 N. University Street West Lafayette, IN 47907-2066 wgautschi@purdue.edu ISBN 978-0-8176-8258-3 DOI 10.1007/978-0-8176-8259-0 Springer New York Dordrecht Heidelberg London e-ISBN 978-0-8176-8259-0 Library of Congress Control Number: 2011941359 Mathematics Subject Classification (2010): 65-01, 65D05, 65D07, 65D10, 65D25, 65D30, 65D32, 65H04, 65H05, 65H10, 65L04, 65L05, 65L06, 65L10 c Springer Science+Business Media, LLC 1997, 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer ScienceCBusiness Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper www.birkhauser-science.com
    TO ERIKA
    Preface to the Second Edition In this second edition, the outline of chapters and sections has been preserved. The subtitle “An Introduction”, as suggested by several reviewers, has been deleted. The content, however, is brought up to date, both in the text and in the notes. Many passages in the text have been either corrected or improved. Some biographical notes have been added as well as a few exercises and computer assignments. The typographical appearance has also been improved by printing vectors and matrices consistently in boldface types. With regard to computer language in illustrations and exercises, we now adopt uniformly Matlab. For readers not familiar with Matlab, there are a number of introductory texts available, some, like Moler [2004], Otto and Denier [2005], Stanoyevitch [2005] that combine Matlab with numerical computing, others, like Knight [2000], Higham and Higham [2005], Hunt, Lipsman and Rosenberg [2006], and Driscoll [2009], more exclusively focused on Matlab. The major novelty, however, is a complete set of detailed solutions to all exercises and machine assignments. The solution manual is available to instructors upon request at the publisher’s website http://www.birkhauser-science.com/978-0-8176- 8258-3. Selected solutions are also included in the text to give students an idea of what is expected. The bibliography has been expanded to reflect technical advances in the field and to include references to new books and expository accounts. As a result, the text has undergone an expansion in size of about 20%. West Lafayette, Indiana November 2011 Walter Gautschi vii
    分享到：
    赞 收藏

    相关推荐

    资料库

    行业

    共收录7266份资料，累计15个分类，关注成员有19位，主要包括：物流,旅游,餐饮零售,网络游戏,咨询,金融,电子政务,外包,教育,制造,医疗,嵌入式,互联网,交通,电信

    热门标签

    物流 旅游 餐饮零售 网络游戏 咨询 金融 电子政务 外包 教育 制造 医疗 嵌入式 互联网 交通 电信

    最新资料