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TitleNumerical Analysis, 9th Edition
Author
LanguageEnglish
File Size14.5 MB
Total Pages895
Table of Contents
                            Cover Page
Half-Title Page
Title Page
Copyright Page
Contents
Preface
	About the Text
	Algorithms and Programs
	New for This Edition
	Supplements
	Possible Course Suggestions
	Acknowledgments
Chapter 1: Mathematical Preliminaries and Error Analysis
	1.1: Review of Calculus
	1.2: Round-off Errors and Computer Arithmetic
	1.3: Algorithms and Convergence
	1.4: Numerical Software
Chapter 2: Solutions of Equations in One Variable
	2.1: The Bisection Method
	2.2: Fixed-Point Iteration
	2.3: Newton’s Method and Its Extensions
	2.4: Error Analysis for Iterative Methods
	2.5: Accelerating Convergence
	2.6: Zeros of Polynomials and Müller’s Method
	2.7: Survey of Methods and Software
Chapter 3: Interpolation and Polynomial Approximation
	3.1: Interpolation and the Lagrange Polynomial
	3.2: Data Approximation and Neville’s Method
	3.3: Divided Differences
	3.4: Hermite Interpolation
	3.5: Cubic Spline Interpolation
	3.6: Parametric Curves
	3.7: Survey of Methods and Software
Chapter 4: Numerical Differentiation and Integration
	4.1: Numerical Differentiation
	4.2: Richardson’s Extrapolation
	4.3: Elements of Numerical Integration
	4.4: Composite Numerical Integration
	4.5: Romberg Integration
	4.6: Adaptive Quadrature Methods
	4.7: Gaussian Quadrature
	4.8: Multiple Integrals
	4.9: Improper Integrals
	4.10: Survey of Methods and Software
Chapter 5: Initial-Value Problems for Ordinary Differential Equations
	5.1: The Elementary Theory of Initial-Value Problems
	5.2: Euler’s Method
	5.3: Higher-Order Taylor Methods
	5.4: Runge-Kutta Methods
	5.5: Error Control and the Runge-Kutta-Fehlberg Method
	5.6: Multistep Methods
	5.7: Variable Step-Size Multistep Methods
	5.8: Extrapolation Methods
	5.9: Higher-Order Equations and Systems of Differential Equations
	5.10: Stability
	5.11: Stiff Differential Equations
	5.12: Survey of Methods and Software
Chapter 6: Direct Methods for Solving Linear Systems
	6.1: Linear Systems of Equations
	6.2: Pivoting Strategies
	6.3: Linear Algebra and Matrix Inversion
	6.4: The Determinant of a Matrix
	6.5: Matrix Factorization
	6.6: Special Types of Matrices
	6.7: Survey of Methods and Software
Chapter 7: IterativeTechniques in Matrix Algebra
	7.1: Norms of Vectors and Matrices
	7.2: Eigenvalues and Eigenvectors
	7.3: The Jacobi and Gauss-Siedel Iterative Techniques
	7.4: Relaxation Techniques for Solving Linear Systems
	7.5: Error Bounds and Iterative Refinement
	7.6: The Conjugate Gradient Method
	7.7: Survey of Methods and Software
Chapter 8: Approximation Theory
	8.1: Discrete Least Squares Approximation
	8.2: Orthogonal Polynomials and Least Squares Approximation
	8.3: Chebyshev Polynomials and Economization of Power Series
	8.4: Rational Function Approximation
	8.5: Trigonometric Polynomial Approximation
	8.6: Fast Fourier Transforms
	8.7: Survey of Methods and Software
Chapter 9: Approximating Eigenvalues
	9.1: Linear Algebra and Eigenvalues
	9.2: Orthogonal Matrices and Similarity Transformations
	9.3: The Power Method
	9.4: Householder’s Method
	9.5: The QR Algorithm
	9.6: Singular Value Decomposition
	9.7: Survey of Methods and Software
Chapter 10: Numerical Solutions of Nonlinear Systems of Equations
	10.1: Fixed Points for Functions of Several Variables
	10.2: Newton’s Method
	10.3: Quasi-Newton Methods
	10.4: Steepest Descent Techniques
	10.5: Homotopy and Continuation Methods
	10.6: Survey of Methods and Software
Chapter 11: Boundary-Value Problems for Ordinary Differential Equations
	11.1: The Linear Shooting Method
	11.2: The Shooting Method for Nonlinear Problems
	11.3: Finite-Difference Methods for Linear Problems
	11.4: Finite-Difference Methods for Nonlinear Problems
	11.5: The Rayleigh-Ritz Method
	11.6: Survey of Methods and Software
Chapter 12: Numerical Solutions to Partial Differential Equations
	12.1: Elliptic Partial Differential Equations
	12.2: Parabolic Partial Differential Equations
	12.3: Hyperbolic Partial Differential Equations
	12.4: An Introduction to the Finite-Element Method
	12.5: Survey of Methods and Software
Bibliography
Answers to Selected Exercises
	Exercise Set 1.1 (Page 14)
	Exercise Set 1.2 (Page 28)
	Exercise Set 1.3 (Page 39)
	Exercise Set 2.1 (Page 54)
	Exercise Set 2.2 (Page 64)
	Exercise Set 2.3 (Page 75)
	Exercise Set 2.4 (Page 85)
	Exercise Set 2.5 (Page 90)
	Exercise Set 2.6 (Page 100)
	Exercise Set 3.1 (Page 114)
	Exercise Set 3.2 (Page 123)
	Exercise Set 3.3 (Page 133)
	Exercise Set 3.4 (Page 142)
	Exercise Set 3.5 (Page 161)
	Exercise Set 3.6 (Page 170)
	Exercise Set 4.1 (Page 182)
	Exercise Set 4.2 (Page 191)
	Exercise Set 4.3 (Page 202)
	Exercise Set 4.4 (Page 210)
	Exercise Set 4.5 (Page 218)
	Exercise Set 4.6 (Page 227)
	Exercise Set 4.7 (Page 234)
	Exercise Set 4.8 (Page 248)
	Exercise Set 4.9 (Page 254)
	Exercise Set 5.1 (Page 264)
	Exercise Set 5.2 (Page 273)
	Exercise Set 5.3 (Page 281)
	Exercise Set 5.4 (Page 291)
	Exercise Set 5.5 (Page 300)
	Exercise Set 5.6 (Page 314)
	Exercise Set 5.7 (Page 320)
	Exercise Set 5.8 (Page 327)
	Exercise Set 5.9 (Page 337)
	Exercise Set 5.10 (Page 347)
	Exercise Set 5.11 (Page 354)
	Exercise Set 6.1 (Page 368)
	Exercise Set 6.2 (Page 379)
	Exercise Set 6.3 (Page 390)
	Exercise Set 6.4 (Page 399)
	Exercise Set 6.5 (Page 409)
	Exercise Set 6.6 (Page 425)
	Exercise Set 7.1 (Page 441)
	Exercise Set 7.2 (Page 449)
	Exercise Set 7.3 (Page 459)
	Exercise Set 7.4 (Page 467)
	Exercise Set 7.5 (Page 476)
	Exercise Set 7.6 (Page 492)
	Exercise Set 8.1 (Page 506)
	Exercise Set 8.2 (Page 518)
	Exercise Set 8.3 (Page 527)
	Exercise Set 8.4 (Page 537)
	Exercise Set 8.5 (Page 546)
	Exercise Set 8.6 (Page 557)
	Exercise Set 9.1 (Page 568)
	Exercise Set 9.2 (Page 573)
	Exercise Set 9.3 (Page 590)
	Exercise Set 9.4 (Page 600)
	Exercise Set 9.5 (Page 611)
	Exercise Set 9.6 (Page 625)
	Exercise Set 10.1 (Page 636)
	Exercise Set 10.2 (Page 644)
	Exercise Set 10.3 (Page 652)
	Exercise Set 10.4 (Page 659)
	Exercise Set 10.5 (Page 666)
	Exercise Set 11.1 (Page 677)
	Exercise Set 11.2 (Page 684)
	Exercise Set 11.3 (Page 689)
	Exercise Set 11.4 (Page 696)
	Exercise Set 11.5 (Page 710)
	Exercise Set 12.1 (Page 723)
	Exercise Set 12.2 (Page 736)
	Exercise Set 12.3 (Page 744)
	Exercise Set 12.4 (Page 758)
Index
Index of Algorithms
Glossary of Notation
Trigonometry
Common Series
The Greek Alphabet
Common Graphs
                        
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