Course material will focus on iterative methods of numerical linear algebra. Both eigenvalue problems and the solution of systems of equations will be covered in detail with emphasis on the algorithms currently used for large scale sparse and structured problems arising from mathematical modelling of real world applications. Links to the mathematical foundation of the methods will be made whenever possible. A solid theoretical background will be balanced with implementation and numerical stability issues.
We emphasize that the courses Math 515 and Math 516 represent an organic sequence. The second part of the sequence can hardly be understood without completing the first one, and skipping the second part would mean that significant portion of time and energy devoted to the first part would have been wasted. It is highly recommended to take the whole sequence.
Textbooks:
N. L. Trefethen and David Bau, III: Numerical Linear Algebra . SIAM, Philadelphia, 1997.
A. Greenbaum: Iterative methods for solving linear systems. SIAM, Philadelphia, 1997.
G. H. Golub and C. F. van Loan: Matrix Computations (Third Edition) . Johns Hopkins University Press, Baltimore and London, 1996.