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.- Course syllabus.
- Instructor: Dr. Sofya Chepushtanova, office SLC 410, email: sofya.chepushtanova@wilkes.edu.
- Class meetings: MWF 12:00-12:50am, room SLC 411 (we will also meet in SLC 409 for labs).
- Office hours: MWF 10:00-10:50am and 2:00-2:50pm or by appointment, SLC 410.
- Textbook: Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms by Anne Greebaum and Timothy Chartier, Princeton University Press, 2012.
- MATLAB is our programming language for this course, it is well suited to linear algebra computations. To start, read Chapter 2 of the textbook. MATLAB is available for use in both labs 409 and 431.
A couple of useful MATLAB resources:
- Here you can find video lectures "Using MATLAB for the First Time" from MIT OpenCourseWare.
-
Numerical Computing with MATLAB
is an archive of MATLAB programs of basic numerical algorithms,
it is good both for beginners and advanced MATLAB programmers.
- LaTeX: a markup language to typeset documents. It excels at making math and the overall layout beautiful. You can use it to type your homework solutions, and I encourage you to do so. Read the tutorial here. You may find the following LaTeX cheat-sheet useful. I will post the LaTeX files for all homework assignments throughout the semester.
- Schedule:
| 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) |
| 2/5 | Continue on Conditioning of Problems; Stability of Algorithms Direct Methods: Gaussian Elimination (Ch. 7) |
Notes on Conditioning/Stability gaussianElim.m lsolve.m |
| 2/12 | Continue on Direct Methods (Ch. 7) Prepare 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 | Conditioning of Linear Systems (Ch. 7). | Notes on Conditioning of Linear Systems Homework 4 due 3/14/18 (click here to download a tex file) |
| 3/5 | Spring Recess 3/3 - 3/11 | |
| 3/12 | Sensitivity of Solutions of Linear Systems. Stability of GE with Partial Pivoting. Least Squares Problems. (Ch. 7) | Notes on Sensitivity of Solutions of Linear Systems Notes on Stability of GE with Partial Pivoting Notes on Least Squares |
| 3/19 | Least Squares Problems (Ch. 7). Singular Value Decomposition |
Notes on SVD Computing SVD: example A cool application of SVD: data compression A video on SVD Tutorial on PCA (optional reading) MatrixTimesCircleIsEllipse.m LowRankApproximations_SVD.m Homework 5 due 3/28/18 (click here to download a tex file) |
| 3/26 | Holiday Recess 3/29 - 4/1 | |
| 4/2 | Iterative Methods: Jacobi, Gauss-Seidel, SOR (Ch. 12). Prepare for Exam II (4/2): study guide | |
| 4/9 | More on Iterative Methods. Conjugate Gradient Algorithm (Ch. 12). |
Notes on Iterative Methods (Jacobi, Gauss-Seidel, Relaxation Techniques) Homework 6 due 4/16/18 (click here to download a tex file) |
| 4/16 | More on Conjugate Gradient Algorithm. | Homework 7 due 4/30/18 (click here to download a tex file) |
| 4/23 | Eigenvalues (Ch. 12): Gerschgorin Theorem; Power Method. MTH 465 students' presentations on Finite Difference Method (Friday, 4/27) |
gersch.m (finds Gerschgorin disks, courtesy of Cory Smithmyer) |
| 4/30 | Prepare for Exam III (5/2): study guide Final Exams begin 5/3 - 5/12 (Wednesday 5/2 follows Friday schedule) | |
| 5/7 | Take-home final exam: due at 10am, Friday, 5/11 (SLC 410) | |