Textbook
-- Instructor's notes
-- 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, singular value decomposition, and eigenvalue problems.  These includes mainly
-- Direct solvers such as pivoting Gaussian elimination, Cholesky factorization;  Condition numbers;
-- Jacobi and Gauss-Seidel iterative methods; Conjugate gradient methods (CG); 
-- QR factorization;  Singular value decomposition (SVD);
-- Numerical methods for eigenvalues of large matrices;
-- Applications to solving ODEs/PDEs and image processing;
-- New topics, e.g., Principal component analysis (PCA).
A major goal of the course is to equip students with the capability to apply and design efficient numerical methods for large scale linear systems in their particular fields.

Homeworks and Class Participation (75%)
There will be five (5) regular homework assignments. 

Final Exam/Project (25%)
Tue. May 7, 2024, 7:30--9:30am (as scheduled by the University). 
This exam may be used as a QE for math students.

Makeups
We follow the rules set by the University.

COVID
We follow the University policies.

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