Newton's Method for Nonlinear Problems Affine Invariance and Adaptive Algorithms Foreign Mathematical Classics Series Facsimile Edition 15

Author: D. Peter
Publisher:
Publish Date: 2006-01-01
Features: This book discusses the numerical solutions of 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 the local and global Newton methods for direct problems and the Gauss-Newton method for inverse problems. The "affine invariance" in this 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 and enables 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. This book discusses the numerical solutions of 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 the local and global Newton methods for direct problems and the Gauss-Newton method for inverse problems. The "affine invariance" in this 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 and enables 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.