Numerical Linear Algebra (Numerical Analysis I)

MTWF 12:00--12:50pm, Weber 15

Instructor

Office: Weber 127

Phone: (970)491-3067

Email: liu@math.colostate.edu

URL:

Office Hour: MWF. 1:00pm--1:50pm and by appointments

__Textbook__

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.

__Homeworks and
Projects (50%)__

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)

Final (30%)

__Makeups__

We shall follow the rules set by the University.

Supplementary Reading

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