MTH 365/465 Numerical Linear Algebra (Spring 2018):

This course provides an introduction to numerical linear algebra, the study of algorithms for finding numerical solutions of linear algebra problems. Topics include direct and iterative methods for the solution of systems of linear equations, matrix decompositions (including singular value decomposition and its applications), computation of eigenvalues and eigenvectors, relaxation techniques, the theoretical basis for error analysis, including vector and matrix norms, applications such as least squares and finite difference methods.
Week of
Topics Class Materials and Assignments

1/15
(no class on 1/15)
Introduction to NLA. Review of important concepts in linear algebra,
Appendix A, pp. 421-435

1/22 Review of important concepts in linear algebra (cont.)
MATLAB basics (Ch. 2)
Floating-Point Representation (Ch. 5)
Intro/Linear Algebra Review notes
On Square Matrices

MATLAB intro lab (.m file)

1/29 Continue on Floating-Point Representation (Ch. 5)
Conditioning of Problems; Stability of Algorithms (Ch. 6)
Notes on Floating-Point Representation

Homework 1 due 2/2/18
(click here to download a tex file)

2/5Continue on Conditioning of Problems; Stability of Algorithms
Direct Methods: Gaussian Elimination (Ch. 7)
Notes on Conditioning/Stability

gaussianElim.m
lsolve.m

2/12Continue on Direct Methods (Ch. 7)

Review for Exam I (2/19): study guide
Notes on Gaussian Elimination
Notes on GE with Pivoting
Handout on GE with pivoting

gaussianElimPivoting.m

Homework 2 due 2/12/18
(click here to download a tex file)

2/19 Cholesky Factorization. Other Methods.
Conditioning of Linear Systems (Ch. 7).
Notes on Cholesky factorization, A.8, § 7.2.4, § 7.3

Handout on Cholesky factorization

Cholesky.m

Homework 3 due 2/21/18
(click here to download a tex file)

2/26

3/5 Spring Recess 3/3 - 3/11

3/12

3/19

3/26 Exam II
Holiday Recess 3/29 - 4/1

4/2

4/9

4/16

4/23 Exam III

4/30 MTH 465 students' presentations
Final Exams begin 5/3 - 5/12
(Wednesday 5/2 follows Friday schedule)

5/7 Take-home final exam due