Classical and modern numerical analysis : theory, methods and practice

Content: 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 Muller'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 Frechet 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 (Nonconvex) 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.