James W. Demmel, Applied Numerical Linear Algebra,
SIAM, 1997, ISBN 0-89871-389-7
Course Contents and Goals
This course covers the design, analysis (accuracy, convergence, stability, and complexity), and implementations of numerical algorithms for solving linear systems, the least squares problems, and eigenvalue problems. These includes, but not limited to, (selected topics from Chapters 1, 2, 4, 5, 6 of the textbook and other books)
Direct solvers such as Pivoting Gaussian Elimination, Chloskey factorization, condition numbers;
Jacobi, Gauss-Seidel iterative methods, Successive Overrelaxation (SOR),
Conjugate Gradients (CG), Krylov subspace methods;
Householder reflections, QR decomposition, Singular value decomposition (SVD);
Power and Inverse methods, QR Iterations, Hessenberg reduction.
Applications to solving partial differential equations, image processing, and data compression will also be discussed. A major goal of the course is to equip students with the capability to apply and design efficient numerical methods for the large scale linear systems in their particular fields.
As graduate students, you are expected to put constant effort on the course during the semester. There will be paper problems for each lecture and some computer projects using Matlab/Fortran/C(++). They are collected every other week. There will be hard problems in the assignments, but I am here to help you any time.
Midterm Exam (20%)
Tentatively scheduled for Fri. Mar. 15, 2019 (class time)
Tentatively scheduled for Wed. May 15, 2019, 4:10pm--6:10pm
We shall follow the rules set by the University.
1. T.A.Davis, "Direct Methods for Sparse Linear Systems", SIAM, 2006, ISBN 0-89871-613-6
2. G.H.Golub and F. Van Loan, "Matrix Computations", 3rd ed., Johns Hopkins Press, 1996, ISBN 0-801-85414-8.
3. Y.Saad, "Iterative Methods for Sparse Linear Systems", 2nd ed., SIAM, 2003, ISBN 0-89871-534-2
4. G.W.Stewart, "Afternotes Goes to Graduate School", SIAM, 1998, ISBN 0-89871-404-4.
5. L.N.Trefethen and D.Bau, "Numerical Linear Algebra", SIAM, 1997, ISBN 0-89871-361-7
Last modified by
J.Liu on Wed.2019/01/16