Classical and modern numerical analysis: theory, methods and practice

Mathematical Review and Computer Arithmetic Mathematical Review Computer Arithmetic Interval ComputationsNumerical Solution of Nonlinear Equations of One Variable Introduction Bisection Method The Fixed Point Method Newton's Method (Newton-Raphson Method) The Univariate Interval Newton MethodSecant Method and Müller's Method Aitken Acceleration and Steffensen's Method Roots of Polynomials Additional Notes and SummaryNumerical Linear Algebra Basic Results from Linear Algebra Normed Linear Spaces Direct Methods for Solving Linear SystemsIterative Methods for Solving Linear SystemsThe Singular Value DecompositionApproximation TheoryIntroduction Norms, Projections, Inner Product Spaces, and Orthogonalization in Function SpacesPolynomial ApproximationPiecewise Polynomial ApproximationTrigonometric ApproximationRational ApproximationWavelet BasesLeast Squares Approximation on a Finite Point SetEigenvalue-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 IntegrationInitial 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 EquationsNumerical Solution of Systems of Nonlinear Equations Introduction and Fréchet Derivatives Successive Approximation (Fixed Point Iteration) and the Contraction Mapping Theorem Newton's Method and VariationsMultivariate Interval Newton MethodsQuasi-Newton Methods (Broyden's Method)Methods for Finding All SolutionsOptimization Local OptimizationConstrained Local Optimization Constrained Optimization and Nonlinear Systems Linear ProgrammingDynamic Programming Global (Nonconvex) OptimizationBoundary-Value Problems and Integral Equations Boundary-Value Problems Approximation of Integral EquationsAppendix: Solutions to Selected ExercisesReferencesIndexExercises appear at the end of each chapter.