Numerical Analysis and Scientific Computation View Larger Image | Jeffery J. Leader
Addison-Wesley, Paperback, Published February 2004, 832 pages, ISBN 0201734990 | List Price: $124.00
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Features
- Quick introduction to numerical methods, with round-off error and computer
arithmetic deferred until students have had experience with real algorithms.
- Modern approach to numerical linear algebra.
- Explanation of numerical techniques from MATLAB and other programs and subroutine
libraries.
- Appropriate mix of numerical analysis theory and practical scientific computation
principles.
- Greater than usual emphasis on optimization.
- Extensive numerical experiments so students can gain experience.
- Efficient and unobtrusive introduction to MATLAB.
Table of
Contents
1. Nonlinear Equations.
Biscetion
and Inverse Linear Interpolation.
Newton's
Method.
The
Fixed Point Theorem.
Quadratic
Convergence of Newton's Method.
Variants
of Newton's Method.
Brent's
Method.
Effects
of Finite Precision Arithmetic.
Newton's
Method for Systems.
Broyden's
Method.
2. Linear Systems.
Gaussian
Elimination with Partial Pivoting.
The
LU Decomposition.
The
LU Decomposition with Pivoting.
The
Cholesky Decomposition.
Condition
Numbers.
The
QR Decomposition.
Householder
Triangularization and the QR Decomposition.
The
Singular Value Decomposition.
3. Iterative Methods.
Jacobi
and Gauss-Seidel Iteration.
Sparsity.
Iterative
Refinement.
Preconditioning.
Krylov
Space Methods.
Numerical
Eigenproblems.
4. Polynomial Interpolation.
Lagrange
Interpolating Polynomials.
Piecewise
Linear Interpolation.
Cubic
Splines.
Computation
of the Cubic Spline Coefficients.
5. Numerical Integration.
Closed
Newton-Cotes Formulas.
Open
Newton-Cotes Formulas and Undetermined Coeffients.
Gaussian
Quadrature.
Gauss-Chebyshev
Quadrature.
Radau
and Lobatto Quadrature.
Adaptivity
and Automatic Integration.
Romberg
Integration.
6. Differential Equations.
Numerical
Differentiation.
Euler's
Method.
Improved
Euler's Method.
Analysis
of Explicit One-Step Methods.
Taylor
and Runge-Kutta Methods.
Adaptivity
and Stiffness.
Multi-Step
Methods.
7. Nonlinear Optimization.
One-Dimensional
Searches.
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.
Afterword.
Bibliography.
Answers.
Index.
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