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Other titles in the Featured Titles for Numerical Analysis series:
Numerical Analysis and Scientific Computationby Jeffrey Leader
Synopses & Reviews
This text emphasizes the mathematical ideas behind the methods and the idea of mixing methods for robustness. The optional use of MATLAB is incorporated throughout the book. This text is intended for a first course in Numerical Analysis taken by students majoring in mathematics, engineering, computer science, or the sciences.
Nonlinear Equations, Linear Systems, Iterative Methods, Polynomial Interpolation, Numerical Integration, Differential Equations, Nonlinear Optimization, Approximation Methods
For all readers interested in numerical analysis and scientific computation.
Book News Annotation:
This is a textbook in numerical analysis and scientific computing intended for students with a year of calculus coursework, and familiarity with matrix algebra and differential equations. Leader prefers not to introduce both mathematical topics and numerical techniques, so all the techniques in this book will be familiar to anyone with the prerequisites listed; for example, Leader chooses not to present the Fourier transform because many students might not be familiar with Fourier analysis. In addition to the usual contents of a textbook like this, there is an emphasis on optimization (displayed by an entire chapter on nonlinear optimization), and optional MATLAB subsections at the end of each subsection.
Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
Table of Contents
1. Nonlinear Equations.
Biscetion and Inverse Linear Interpolation.
The Fixed Point Theorem.
Quadratic Convergence of Newton's Method.
Variants of Newton's Method.
Effects of Finite Precision Arithmetic.
Newton's Method for Systems.
2. Linear Systems.
Gaussian Elimination with Partial Pivoting.
The LU Decomposition.
The LU Decomposition with Pivoting.
The Cholesky Decomposition.
The QR Decomposition.
Householder Triangularization and the QR Decomposition.
Gram-Schmidt Orthogonalization and the QR Decomposition.
The Singular Value Decomposition.
3. Iterative Methods.
Jacobi and Gauss-Seidel Iteration.
Krylov Space Methods.
4. Polynomial Interpolation.
Lagrange Interpolating Polynomials.
Piecewise Linear Interpolation.
Computation of the Cubic Spline Coefficients.
5. Numerical Integration.
Closed Newton-Cotes Formulas.
Open Newton-Cotes Formulas and Undetermined Coeffients.
Radau and Lobatto Quadrature.
Adaptivity and Automatic Integration.
6. Differential Equations.
Improved Euler's Method.
Analysis of Explicit One-Step Methods.
Taylor and Runge-Kutta Methods.
Adaptivity and Stiffness.
7. Nonlinear Optimization.
The Method of Steepest Descent.
Newton Methods for Nonlinear Optimization.
Multiple Random Start Methods.
Direct Search Methods.
The Nelder-Mead Method.
Conjugate Direction Methods.
8. Approximation Methods.
Linear and Nonlinear Least Squares.
The Best Approximation Problem.
Best Uniform Approximation.
Applications of the Chebyshev Polynomials.
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