Content: Course will cover iterative methods for large-scale linear systems of equations. Topics will include matrix splittings and stationary iterations, Krylov subspace methods, preconditioning techniques, multilevel methods, and selected applications. If time allows, iterative methods for eigenvalue problems will also be covered. Particulars: familiarity with numerical linear algebra and Matlab programming, such as provided by Math 515 - Numerical Analysis I, is assumed.
Textbook and other reading material:
A. Bjorck, Numerical Methods in Matrix Computations. Texts in Applied Mathematics 59, Springer, 2015.
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd Edition. Society for Industrial and Applied Mathematics, 2003.
Slides, part I
Slides, part II
Slides, part III
Slides, part IV
M. Benzi, Preconditioning Techniques for Large Linear Systems: A Survey, Journal of Computational Physics, 182 (2002), pp. 418-477.
M. Benzi, G. H. Golub, and J. Liesen, Numerical Solution of Saddle Point Problems, Acta Numerica, 14 (2005), pp. 1-137.
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