# Math 270A -- Numerical Linear Algebra -- Fall 2018

## Homework

1. Homework 1 - Solutions 1
2. Homework 2 - Solutions 2
3. Optional Programming Homework 1 - Python script
4. Homework 3 - Solutions 3
5. Optional Programming Homework 2 - C Code
6. Homework 4 - Solutions 4
7. Homework 5 - Solutions 5

## Course Calendar

Lecture Content
# 1, 0F
28.09.2018.
Administrative. Outline of Numerical Linear Algebra. I.1: Simple algorithms. Homework 1 announced. Intro Slides
# 2, 1M
01.10.2018.
I.2: Solving triangular systems of equations.
# 3, 1W
03.10.2018.
I.3: Inverting triangular matrices. I.4: LU decomposition.
# 4, 1F
05.10.2018.
I.4: LU decomposition, continued.
# 5, 2M
08.10.2018.
I.5: LU decomposition with pivoting.
# 6, 2W
10.10.2018.
I.5: LU decomposition with pivoting, Diagonally dominant matrices.
# 7, 2F
12.10.2018.
I.6: LDLT decomposition. SPD matrices. Homework 1 collected. Homework 2 announced.
# 8, 3M
15.10.2018.
I.7: Cholesky factorization. II.1: QR decomposition.
# 9, 3W
17.10.2018.
II.2: Gram-Schmidt orthogonalization.
# 10, 3F
19.10.2018.
II.3: QR decomposition using Givens rotations.
#11, 4M
22.10.2018.
II.3: QR decomposition using Givens rotations. II.4: QR decomposition using Householder reflections.
#12, 4W
24.10.2018.
II.5: Least-Squares Problems of Full Rank.
#13, 4F
26.10.2018.
II.5: Least-Squares Problems of Full Rank. Homework 2 collected. Homework 3 announced.
#14, 5M
29.10.2018.
III.1 Least-Squares Problems and their solvability. III.2 Least-Squares Problems and the Pseudoinverse.
#15, 5W
31.10.2018.
III.3 Schur decomposition and Singular Value Decomposition.
#16, 5F
02.11.2018.
III.3 Singular Value Decomposition and Pseudoinverse
#17, 6M
05.11.2018.
III.3 Direct Methods recapitulated. Direct Method Slides IV.1: Banach fixpoint theorem
#18, 6W
07.11.2018.
IV.2: Classical iterative methods via fixpoint theory, Spectral radius, and Convergence theory.
#19, 6F
09.11.2018.
IV.3: Gerschgorin circle theorem. Convergence of classical Richardson iteration. Homework 3 collected. Homework 4 announced.
#20, 7M
12.11.2018.
Veteran's Day Holiday
#21, 7W
14.11.2018.
IV.4: Jacobi method and Gauss-Seidel method.
#22, 7F
16.11.2018.
IV.5: Over-relaxation methods.
#23, 8M
19.11.2018.
V.1: Gradient descent and its convergence.
#24, 8W
21.11.2018.
V.1: Gradient descent and its convergence.
#25, 8F
23.11.2018.
Thanksgiving Holiday
#26, 9M
26.11.2018.
V.2: Method of Conjugate Gradients. Homework 4 collected. Homework 5 announced.
#27, 9W
28.11.2018.
#28, 9F
30.11.2018.
VI.1 Eigenvalue Problems via Power Iteration