Lecture Notes Nonlinear Equations

Lecture Notes on Nonlinear Systems of Equations

Preliminary material (norms, inner products, rate of convergence)
Introduction (discussion of basic issues, convergence of Newton, line-search, stopping criteria)
Newton with Gaussian elimination (exact Newton, finite difference, Jacobian, exploiting sparsity)
Newton-Krylov methods (soon)
Broyden's method

Lecture Notes on Large, Sparse Eigenvalue Problems

Introduction (basics - chapter 1 sections 1 and 2 and chapter 4 section 1)
Perturbation Theory (chapter 1 section 3 and chapter 4 section 2)
Overview of Methods (for this course)
Krylov subspaces and Rayleigh-Ritz approximation (chapter 4 sections 3 and 4)
Krylov sequence methods, Arnoldi and Lanczos methods and variants (implicitly restarted Arnoldi/Lanczos
Newton-based methods, Jacobi-Davidson method, Davidson's method

Large, sparse, eigenvalue problems and sensitivity/accuracy of eigenvalue problems

(from Summer School organized by the Materials Computation Center )

Derivation of Methods
Sensitivity and Accuracy

Numerical Linear Algebra

Useful material based on David Watkins, Fundamentals of Matrix Computations (2nd ed.), Wiley:

Intro
Overview
Chapters 1 and 2 - Solving Linear Systems of Equations
Chapter 3 - Overdetermined Systems
Chapter 4 - Singular Value Decomposition
Chapter 5 - Eigenvalue Problems Part I
Chapter 5 - Eigenvalue Problems Part II (more fun stuff to be added)