Lecture Notes on Iterative Methods
Lecture Notes:

Introduction (13 MB)

Synopsis of Numerical Linear Algebra (more extensive notes are below)

FixedPoint Iterations, Krylov Spaces, and Krylov Methods

Comparing CG and GMRES for Various Model Problems

Convergence of CG – part I

Convergence of CG – part II: local convergence

Convergence of MINRES and GMRES

Generalizations of (restarted) GMRES

Methods based on the twosided Lanczos algorithm

Preconditioners based on incomplete factorizations

SaddlePoint preconditioners

Domain decomposition preconditioners  for convergence theory see notes from class)

Multigrid 1 – basic iterative methods and error smoothing

Multigrid 2 – smooth and oscillatory modes, basic multigrid

Multigrid 3 – local mode analysis

Multigrid 4 – convergence proof and analysis
Background Material:
Lecture notes (by EdS) based on David Watkins, Fundamentals
of Matrix Computations (2nd ed.), Wiley:
Lecture notes (by Mike Heath) based on Michael T. Heath,
Scientific Computing: An Introductory Survey (2nd ed.), McGrawHill:
The linear algebra chapters of this book provide some useful background material.
Lecture notes (EdS) on Numerical Partial Differential Equations (soon)
Discretized PDEs will be used as test problems and benchmarks for understanding various aspects of linear solvers and solvers for eigenvalue problems.