Lecturer: Matthias Maier
Teaching assistant: Jingyan Zhang
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Lecture notes will be made available online on eCampus. There is no textbook for
References: Iterative Methods for Sparse Linear Systems by Yousef Saad. Iterative methods for solving linear systems by Anne Greenbaum.
The goal of this course is to provide an introduction to the development and analysis of iterative methods applied to the solution of large sparse systems of linear equations. Such systems often arise in large scale scientific computations involving the modeling of complex physical processes. We will start with basic analysis of iterative methods including classical examples such as Richardson's method, the Jacobi method, the Gauss-Siedel method and the successive over relaxation (SSOR) method. Next, the acceleration of SSOR will be studied as well as acceleration by the use of Krylov subspace techniques. The most useful Krylov subspace methods, namely, the steepest descent method, the conjugate gradient method, the minimal residual method and the generalized minimal residual method will be considered. Along the way, we will introduce preconditioning and develop preconditioned versions of many of the methods discussed above. Time permitting, we shall consider either the development of preconditioners by domain decomposition or multigrid or the application of iterative methods to saddle point problems.
A fundamental ingredient in any course on iterative methods involves implementation which is to be done in MATLAB. (Matlab is available at a discounted rate for students, see here. Octave is an open source alternative.) There is a lab component for this course. TBA