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Classical and Modern Numerical Analysis: Theory, Methods and Practice

Azmy S Ackleh, Edward James Allen, Ralph Baker Hearfott, and Padmanabhan Seshaiyer
Publisher: 
Chapman & Hall/ CRC
Publication Date: 
2009
Number of Pages: 
608
Format: 
Hardcover
Series: 
Chapman & Hall/ CRC Numerical Analysis and Scientific Computing
Price: 
99.95
ISBN: 
9781420091571
Category: 
Textbook
We do not plan to review this book.

Mathematical Review and Computer Arithmetic

Mathematical Review

Computer Arithmetic

Interval Computations

Numerical Solution of Nonlinear Equations of One Variable

Introduction

Bisection Method

The Fixed Point Method

Newton’s Method (Newton–Raphson Method)

The Univariate Interval Newton Method

Secant Method and Müller’s Method

Aitken Acceleration and Steffensen’s Method

Roots of Polynomials

Additional Notes and Summary

Numerical Linear Algebra

Basic Results from Linear Algebra

Normed Linear Spaces

Direct Methods for Solving Linear Systems

Iterative Methods for Solving Linear Systems

The Singular Value Decomposition

Approximation Theory

Introduction

Norms, Projections, Inner Product Spaces, and Orthogonalization in Function Spaces

Polynomial Approximation

Piecewise Polynomial Approximation

Trigonometric Approximation

Rational Approximation

Wavelet Bases

Least Squares Approximation on a Finite Point Set

Eigenvalue-Eigenvector Computation

Basic Results from Linear Algebra

The Power Method

The Inverse Power Method

Deflation

The QR Method

Jacobi Diagonalization (Jacobi Method)

Simultaneous Iteration (Subspace Iteration)

Numerical Differentiation and Integration

Numerical Differentiation

Automatic (Computational) Differentiation

Numerical Integration

Initial Value Problems for Ordinary Differential Equations

Introduction

Euler’s Method

Single-Step Methods: Taylor Series and Runge–Kutta

Error Control and the Runge–Kutta–Fehlberg Method

Multistep Methods

Predictor-Corrector Methods

Stiff Systems

Extrapolation Methods

Application to Parameter Estimation in Differential Equations

Numerical Solution of Systems of Nonlinear Equations

Introduction and Fréchet Derivatives

Successive Approximation (Fixed Point Iteration) and the Contraction Mapping Theorem

Newton’s Method and Variations

Multivariate Interval Newton Methods

Quasi-Newton Methods (Broyden’s Method)

Methods for Finding All Solutions

Optimization

Local Optimization

Constrained Local Optimization

Constrained Optimization and Nonlinear Systems

Linear Programming

Dynamic Programming

Global (Non-Convex) Optimization

Boundary Value Problems and Integral Equations

Boundary Value Problems

Approximation of Integral Equations

Appendix: Solutions to Selected Exercises

References

Index

Exercises appear at the end of each chapter.

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