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Methods for Solving Systems of Nonlinear Equations

Methods for Solving Systems of Nonlinear Equations

2nd Edition

£45.99

Part of CBMS-NSF Regional Conference Series in Applied Mathematics

  • Date Published: September 1998
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898714159

£ 45.99
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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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.

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    Product details

    • Edition: 2nd Edition
    • Date Published: September 1998
    • format: Paperback
    • isbn: 9780898714159
    • length: 184 pages
    • dimensions: 253 x 178 x 10 mm
    • weight: 0.298kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    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.

  • Author

    Werner C. Rheinboldt, University of Pittsburgh

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