Click Here to Download: https://ouo.io/75CicW6 Newton Methods for Nonlinear Problems Affine Invariance and Adaptive Algorithms By: Peter Deuflhard Publisher: Springer Print ISBN: 9783642238987, 364223898X eText ISBN: 9783642238994, 3642238998 Copyright year: 2011 Format: PDF Available from $ 79.99 USD SKU 9783642238994 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.
