Affine Invariance of Newton's Method for Nonlinear Problems and Adaptive Algorithms (Photocopy Edition)

Author: Peter Deuflhard
Publisher:
Publish Date: 2006-01-17
Features: This book discusses numerical methods for nonlinear problems in science and engineering, including finite-dimensional systems (algebraic systems) and infinite-dimensional systems (ordinary differential equations and partial differential equations). It focuses on local and global Newton methods for direct problems and Gauss-Newton methods for inverse problems. The "affine invariance" in the book refers to the invariance of the algorithms and their convergence under four types of affine transformations. Compared to traditional textbooks, the unique approach of using "affine invariance" for discussion makes theorems and proofs more concise, enabling the construction of fully adaptive algorithms. Numerous numerical examples, comparison charts, and exercises make this book highly suitable for computational mathematics courses; at the same time, it opens up many possible directions for future research.