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PRINTED BOOKS
Author Deuflhard, P. (Peter)

Title Newton methods for nonlinear problems : affine invariance and adaptive algorithms / Peter Deuflhard.

Published Berlin ; New York : Springer, [2004]
©2004

Copies

Location Call No. Status
 UniM ERC  518.26 DEUF    AVAILABLE
Physical description xii, 424 pages : illustrations ; 25 cm.
Series Springer series in computational mathematics, 0179-3632 ; 35.
Springer series in computational mathematics. 0179-3632 ; 35.
Bibliography Includes bibliographical references (pages [405]-415) and index.
Contents 1. Introduction -- 2. Systems of equations : local Newton methods -- 3. Systems of equations : global Newton methods -- 4. Least squares problems : Gauss-Newton methods -- 5. Parameter dependent systems : continuation methods -- 6. Stiff ODE initial value problems -- 7. ODE boundary value problems -- 8. PDE boundary value problems.
Summary "This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss - Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational math classes. At the same time, the book opens many directions for possible future research."--BOOK JACKET.
Subject Numerical analysis.
Algebras, Linear.
Equations, Theory of.
ISBN 3540210997 (acid-free paper)
3540210997 (acid-free paper) No price