# MA/CSC 580 - Numerical Analysis I

You can download the course information here.

More information can be found on the course Moodle page.

**References**:

- I. C. F. Ipsen, Numerical Matrix Analysis, SIAM, 2009.
- C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM, 1995.
- D. Watkins, Fundamentals of Matrix Computations, Wiley-Blackwell, 2002.

## Fall 2023 Tentative Course Schedule

### Week 1

- 08/22 Lecture 1: Welcome and Course Overview; Review of Linear Algebra

- 08/24 Lecture 2: Review of Linear Algebra, Vector Norms

### Week 2

- 08/29 Lecture 3: Matrix Norms

- 08/31 Lecture 4: Matrix Norms II, Errors and Floating-Point System

### Week 3

- 09/05 Lecture 5: Conditioning of Subtraction, Banach Lemma
- 09/07 Lecture 6: Conditioning of matrix inverse, linear systems

** Homework 1 due Tuesday

### Week 4

- 09/12 Lecture 7: Conditioning of linear systems, LU factorization
- 09/14 Lecture 8: Pivoted LU Factorization

### Week 5

- 09/19 Wellness Day. No Class.
- 09/21 Lecture 9: Cholesky factorization

** Homework 2 due Monday

### Week 6

- 09/26 Lecture 10: Sparsity, Least Squares: Normal Equations
- 09/28 Lecture 11: QR factorization; Givens

### Week 7

- 10/03 Lecture 12: Gram-Schmidt; Householder; Summary of QR
- 10/05 Lecture 13: SVD

** Homework 3 due Thursday

### Week 8

- 10/10 Fall break; No class
- 10/12 Lecture 14: SVD II; Review

### Week 9

- 10/17 Midterm Exam
- 10/19 Lecture 15: SVD and Least Squares. Sensitivity of Least Squares.

** Homework 4 due Friday

### Week 10

- 10/24 Lecture 16: SVD III
- 10/26 Lecture 17: Eigenvalues and eigenvectors, Eigendecompositions

### Week 11

- 10/31 Lecture 18: Power methods
- 11/02 Lecture 19: Rayleigh Quotient, QR iteration

### Week 12

- 11/07 Lecture 20: Stationary Iterative Methods
- 11/09 Lecture 21: Krylov subspaces; Arnoldi; GMRES

** Homework 5 due Wednesday

### Week 13

- 11/14 Lecture 22: GMRES, Conjugate Gradient
- 11/16 Lecture 23: Conjugate Gradient II

### Week 14

- 11/21 Lecture 24: Preconditioning
- 11/23 Thanksgiving Holiday; No class

### Week 15

- 11/28 Lecture 25: Nonlinear Equations, Newton’s method
- 11/30 Lecture 26: Special topic: Intro to Deep Learning

** Homework 6 due Friday

### Week 16

- 12/05 Lecture 27: Review

** 12/06: Reading Day