MA 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 2022 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
08/26 Lecture 3: Vector Norms

Week 2

08/29 Lecture 4: Matrix Norms
08/31 Lecture 5: Matrix Norms II
09/02 Lecture 6: Errors and Floating-Point System

** Homework 1 due Friday

Week 3

09/05 Labor Day; No class
09/07 Lecture 7: Conditioning of Subtraction, Banach Lemma
09/09 Lecture 8: Conditioning of matrix inverse, linear systems

Week 4

09/12 Lecture 9: Conditioning of linear systems, LU factorization
09/14 Lecture 10: Pivoted LU Factorization
09/16 Lecture 11: Pivoted LU Factorization II

** Homework 2 due Friday

Week 5

09/19 Lecture 12: PLU and Stability.
09/21 Lecture 13: Cholesky factorization
09/23 Lecture 14: Cholesky factorization II

Week 6

09/26 Lecture 15: Sparsity
09/28 Lecture 16: Least Squares: Normal Equations
09/30 Lecture 17: QR factorization; Givens

** Homework 3 due Friday

Week 7

10/03 Lecture 18: Gram-Schmidt.
10/05 Lecture 19: Gram-Schmidt; Householder
10/07 Lecture 20: Summary of QR; SVD

Week 8

10/10 Fall break; No class
10/12 Lecture 21: SVD - Alternative forms; Review
10/14 Lecture 22: Midterm Exam

Week 9

10/17 Lecture 23: SVD: Existence and Norms
10/19 Lecture 24: SVD and Least Squares.
10/21 Lecture 25: Sensitivity of Least Squares; Summary

** Homework 4 due Friday

Week 10

10/24 Lecture 26: Stationary Iterative Methods
10/26 Lecture 27: Stationary Iterative Methods; Krylov subspaces
10/28 Lecture 28: Arnoldi; GMRES

Week 11

10/31 Lecture 29: Convergence of GMRES
11/02 Lecture 30: Conjugate Gradient
11/04 Lecture 31: Convergence of CG

** Homework 5 due Friday

Week 12

11/07 Lecture 32: Preconditioning
11/09 Lecture 33: Nonlinear Equations, Newton’s method
11/11 Lecture 34: Newton’s method and Inexact Newton’s method

Week 13

11/14 Lecture 35: Eigenvalues and eigenvectors
11/16 Lecture 36: Eigendecompositions, perturbation theory
11/18 Lecture 37: Bauer-Fike, Power methods

** Homework 6 due Friday

Week 14

11/21 Lecture 38: Rayleigh Quotient, QR iteration
11/23, 11/25 Thanksgiving Holiday; No class

Week 15

11/28 Lecture 39: Large-scale eigenvalue problems
11/30 Lecture 40: Special topic
12/02 Lecture 41: Special topic II

** Homework 7 due Friday

Week 16

12/05 Lecture 42: Review

** 12/06 -12/07: Reading Days