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9780898714159 Academic Inspection Copy

Methods for Solving Systems of Nonlinear Equations

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This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs. Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization methods. New information on parametrized equations and continuation incorporates research since the first edition.
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.
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