Week 1   21-25 August
08/21 --- Overview of Scientific Computation;
08/23 --- Floating point Arithmetic & Error bounds;
08/25 --- Algorithm & Complexity.

Week 2   28 August-1 September
08/28 --- Gauss Elimination & Triangular decomposition;
08/30 ---  Pivoting & Complexity;
09/01 --- The  Cholesky decomposition;

Week 3  4-8 September
09/04 --- (no class) University Holiday
09/06 --- The QR decomposition of householder;
09/08 --- The householder  algorithm;

Week 4  11-15 September
09/11 ---Complexity comparisons; 
09/13 --- Norms of Vector and  Matrix;
09/15 --- Error bounds;

Week 5   18-22  September
09/18 --- Ill-conditioned problems.
09/20 --- SVD  and Pseudo-normal solution;
09/22 --- Summary of $Ax=b$.

Week 6  25-- 29  September
09/25 --- The Householder method;
09/27 --- Eigenvalues for Hessenberg Matrix;
09/29 --- Jacobi-rotation  & Eigenvalue estimates;

Week 7  2-6 October
10/02 ---The power method. 
10/04 --- The Rayleigh quotient; 
10/06 ---  The  QR Algorithms 

Week 8   9-13 October
10/09 --- Midterm
10/11 ---  The practical QR Algorithms
10/13 --- Summary of eigenvalue solver (second half semester begins)

Week 9   16-20 October
10/16 --- General iteration methods and their convergence;
10/18 ---  Stationary iterative methods for Ax=b (Matrix splitting )
10/20 --- The Jacobi  &  The Gauss-Seidel method, SOR

Week 10   23-27 October
10/23 ---  Convergence of Jacobi-Gauss-Seidel-SOR family
10/25 --- The Krylov subspace method 
10/27 ---  The Conjugate gradient method

Week 11  30 October -3 November
10/30 --- Convergence of the CG method;
11/01 --- Preconditioner;
11/03 --- Other Krylov subspace methods (CGNR, CGNE);

Week 12  6-10 November
11/06--- GMRES iteration
11/08 --- Nonlinear problems
11/10 --- 1-D variation of Newton's methods; 

Week 13  13-17 November
11/13 --- Newton's method for F(x)=0;
11/15 --- Newton method for unconstrained optimization;
11/17 --- Quasi-Newton and Broyden's method;

*** Thanksgiving Break 20-24 November ***

Week 14   27 November-01  December
11/27 --- Global convergent strategy and fast local strategy;
11/29 ---  Line Search Algorithm;
12/01 --- More on global convergence. 

Week 15  4-8 December
12/04 --- Review 1
12/06 --- Review 2
12/08 --- Final discussion

Final Week  11--15 December