Numerical Analysis

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  • Edition: 5th
  • Format: Paperback
  • Copyright: 1996-09-25
  • Publisher: Brooks Cole
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This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition.

Table of Contents

Mathematical preliminaries
Review of Calculus
Round-off Errors and Computer Arithmetic
Algorithms and Convergence
Numerical Software
Solutions of equations in one variable
The Bisection Method. Fixed-Point Iteration
The Newton's Method
Error Analysis for Iterative Methods
Accelerating Convergence
Zeros of Polynomials and Muller's Method
Survey of Methods and Software
Interpolation and polynomial approximation
Interpolation and the LaGrange Polynomial
Divided Differences
Hermite Interpolation
Cubic Spline Interpolation
Parametric Curves
Survey of Methods and Software
Numerical differentiation and integration
Numerical Differentiation
Richardson's Extrapolation
Elements of Numerical Integration
Composite Numerical Integration
Romberg Integration
Adaptive Quadrature Methods
Gaussian Quadrature
Multiple Integrals
Improper Integrals
Survey of Methods and Software
Initial-value problems for ordinary differential equations
The Elementary Theory of Initial-Value Problems
Euler's Method
Higher-Order Taylor Methods
Runge-Kutta Methods
Error Control and the Runge-Kutta-Fehlberg Method
Multi-Step Methods
Variable Step-Size Multi-Step Methods
Extrapolation Methods
Higher-Order Equations and Systems of Differential Equations
Stability. Stiff Differential Equations
Survey of Methods and Software
Direct methods for solving linear systems
Linear Systems of Equations
Pivoting Strategies
Linear Algebra and Matrix Inversion
The Determinant of a Matrix
Matrix Factorization
Special Types of Matrices
Survey of Methods and Software
Iterative techniques in matrix algebra
Norms of Vectors and Matrices
Eigenvalues and Eigenvectors
Iterative Techniques for Solving Linear Systems
Error Bounds and Iterative Refinement
The Conjugate Gradient Method
Survey of Methods and Software
Approximation theory
Discrete Least Squares Approximation
Orthogonal Polynomials and Least Squares Approximation
Chebyshev Polynomials and Economization of Power Series
Rational Function Approximation
Trigonometric Polynomial Approximation
Fast Fourier Transforms
Survey of Methods and Software
Approximating eigenvalues
Linear Algebra and Eigenvalues
The Power Method
Householder's Method
The QR Algorithm
Survey of Methods and Software
Numerical solutions of nonlinear systems of equations
Fixed Points for Functions of Several Variables
Newton's Method
Quasi-Newton Methods
Steepest Descent Techniques
Homotopy and Continuation Methods
Survey of Methods and Software
Boundary-value problems for ordinary differential equations
The Linear Shooting Method
The Shooting Method for Nonlinear Problems
Finite-Difference Methods for Linear Problems
Finite-Difference Methods for Nonlinear Problems
The Rayleigh-Ritz Method
Survey of Methods and Software
Numerical solutions to partial differential equations
Elliptic Partial-Differential Equations
Parabolic Partial-Differential Equations
Hyperbolic Partial-Differential Equations
An Introduction to the Finite-Element Method
Survey of Methods and Software
Answers to Selected Exercises
Table of Contents provided by Publisher. All Rights Reserved.

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