Methods for Solving Systems of Nonlinear Equations

Preface to the Second Edition Preface to the First Edition Chapter 1: Introduction. Problem Overview Notation and Background Chapter 2: Model Problems. Discretization of Operator Equations Minimization Discrete Problems Chapter 3: Iterative Processes and Rates of Convergence. Characterization of Iterative Processes Rates of Convergence Evaluation of Convergence Rates On Efficiency and Accuracy Chapter 4: Methods of Newton Type. The Linearization Concept Methods of Newton Form Discretized Newton Methods Attraction Basins Chapter 5: Methods of Secant Type. General Secant Methods Consistent Approximations Update Methods Chapter 6: Combinations of Processes. The Use of Classical Linear Methods Nonlinear SOR Methods Residual Convergence Controls Inexact Newton Methods Chapter 7: Parametrized Systems of Equations. Submanifolds of R n Continuation Using ODEs Continuation with Local Parametrizations Simplicial Approximations of Manifolds Chapter 8: Unconstrained Minimization Methods. Admissible Step Length Algorithms Gradient Related Methods Collectively Gradient Related Directions Trust Region Methods Chapter 9: Nonlinear Generalizations of Several Matrix Classes. Basic Function Classes Properties of the Function Classes Convergence of Iterative Processes Chapter 10: Outlook at Further Methods. Higher Order Methods Piecewise-Linear Methods Further Minimization Methods Bibliography Index.