Newton Methods for Nonlinear Problems

Focusing on efficient numerical solutions for complex nonlinear problems in both finite and infinite dimensions, this book emphasizes local and global Newton methods for direct problems and Gauss-Newton methods for inverse problems. The unique concept of 'affine invariance' allows for algorithmic and convergence analysis that adapts to various affine transformations, resulting in concise theorems and proofs. With numerous numerical illustrations, comparison tables, and exercises, it serves as a valuable resource for computational mathematics and inspires future research opportunities.