Lecture 
Date 
Topics 
Complementary
Readings 
Notes 
1 
Sept 13 
Introduction, LU factorization (Lecture slides) 
[TB] Chapter 1, pages 110 [TB] Chapter 20, pages 147152 

2 
Sept 15 
Cholesky factorization, tridiagonal, band matrices (Lecture slides)  [TB] Chapter 12. pages 172176 

3 
Sept 20 
1D, 2D Laplacian (Lecture slides) 
[Saad] Chapter 2

A1 out 
4 
Sept 22 
Sparse Gaussian Elimination,
graph representation (Lecture slides) 
[Saad] Sect 3.13.2  
5 
Sept 27 
Ordering methods (Lecture slides) 
[Saad] Sect 3.3  
6 
Sept 29 
Stability and image denoising (Lecture slides) 
[TB] Chapter 22, pages 163170  
7 
Oct 4 
Image denoising and iterative
methods (Lecture slides) 


8 
Oct 6 
Iterative methods and steepest
descent (Lecture slides) 
[Saad] Chapter 4 
A1 due A2 out 
9 
Oct 11 
Conjugate
gradient (Lecture slides) 
[TB] Chapter 38, pages 293301 [Saad] Sect 5.3 and 6.7 

10 
Oct 13 
Least squares problems (Lecture slides) 
[TB] Chapter 11  
11 
Oct 18 
QR Factorization and
GramSchmidt orthogonalization (Lecture
slides) 
[TB] Chapters 7, 8  
12 
Oct 20 
Householder reflections and
Givens rotations (Lecture slides) 
[TB] Chapter 10  
13 
Oct 25 
Singular value decomposition and
conditioning (Lecture slides) 
[TB] Chapters 4, 12  A2 due A3 out 
14 
Oct 27 
Eigenvalue problems (Lecture slides)  [TB] Chapter 24, 25, 26  
15 
Nov 1 
Rayleigh Quotient Algorithm and
QR Algorithm (Lecture slides) 
[TB] Chapter 27, 28  
Midterm 
Nov 3 

17 
Nov 8 
QR algorithm and reduction to
Hessenberg (Lecture slides) 
[TB] Chapter 28  
18 
Nov 10 
QR method with shifts, Google
PageRank (Lecture slides) 
[TB] Chapter 29  
Midterm review 
Nov 15 
A3 due A4 out 

20 
Nov 17 
Singular value decomposition (Lecture slides) 
[TB] Chapter 31 

21 
Nov 22 
Bidiagonalization, SVD Image
Compression (Lecture slides) 
[TB] Chapter 31 

22 
Nov 24 
Search engine using SVD (Lecture slides) 

23 
Nov 29 
Convergence of iterative methods
(Lecture slides) 

24 
Dec 1 
Convergence of conjugate
gradient (Lecture slides) 
A4 due 