Newton Methods for Nonlinear Problems

Affine Invariance and Adaptive Algorithms

  • Peter Deuflhard

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 35)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Peter Deuflhard
    Pages 7-41
  3. Algebraic Equations

    1. Front Matter
      Pages 43-43
    2. Peter Deuflhard
      Pages 45-107
    3. Peter Deuflhard
      Pages 109-172
    4. Peter Deuflhard
      Pages 173-231
  4. Differential Equations

    1. Front Matter
      Pages 283-283
    2. Peter Deuflhard
      Pages 285-314
    3. Peter Deuflhard
      Pages 315-368
    4. Peter Deuflhard
      Pages 369-404
  5. Back Matter
    Pages 405-424

About this book


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 mathematics classes. At the same time, the book opens many directions for possible future research.


Gauss-newton methods Newton methods affine invariance continuation methods differential equations

Authors and affiliations

  • Peter Deuflhard
    • 1
  1. 1.Zuse-Institut Berlin (ZIB)BerlinGermany

Bibliographic information