Methods for Solving Systems of Nonlinear Equations

Preface to the second edition; Preface to the first edition; 1. Introduction: Problem overview; Notation and background; 2. Model problems: discretization of operator equations; Minimization; Discrete problems; 3. Iterative processes and rates of convergence: Characterization of iterative processes; Rates of Convergence; Evaluation of convergence rates; On Efficiency and Accuracy; 4. Methods of Newton type: the linearization concept; Methods of Newton form; Discretized Newton methods; Attraction basins; 5. Methods of secant type: general Secant methods; Consistent approximations; Update methods; 6. Combinations of processes: the use of classical linear methods; Nonlinear SOR Methods; Residual convergence controls; Inexact Newton methods; 7. Parametrized systems of equations: Submanifolds of Rn; Continuation using ODEs; Continuation with local parametrizations; Simplicial approximations of manifolds; 8. Unconstrained minimization methods: admissible step length algorithms; Gradient related methods; Collectively gradient related directions; Trust region methods; 9. Nonlinear generalizations of several matrix classes: basic function classes; Properties of the function classes; Convergence of iterative processes; 10. Outlook at further methods: higher order methods; Piecewise-linear methods; Further minimization methods; Bibliography; Index.