###EE 636 – MATRIX COMPUTATIONS

Semester

Spring’14.

Instructor

Professor Madhu Bellur.

Motivation

Any mathematical operation implemented on a computational software (e.g. MatLab), is carried out using a matrix as the basic storage cell and exploiting results from the matrix theory for manipulating them. This course is rigorous in such matrix algorithms.

Content

Basic iterative methods for solutions of linear systems and their rates of convergence. Generalized conjugate gradient, Krylov space and Lanczos methods. Iterative methods for symmetric, non-symmetric and generalized eigenvalue problems. Singular value decompositions. Fast computations for structured matrices. Polynomial matrix computations. Perturbation bounds for eigenvalues.

Pre requisites

None.

Feedback on lectures

Since matrix theory is an immensely vast area, it’s in the best interest to attend lectures to avoid skimming through a huge list of texts right before the exams. Since it is an algorithm-rich course, it is very important to get a complete understanding of these and attending lectures is the best and the easiest way to go about doing this.

Feedback on quizzes and exams

The exams are fairly easy and test the completeness of one’s understanding. Very much based on what has been discussed/covered in the class. So missing lectures is a big loss.

Grading

Moderate.

AA	5
AB	8
AU	2
BB	11
BC	18
CC	4
CD	3
FR	6
Total	57

Attendance

No policy.

Future direction

Helps convey a fundamental understanding of how computational tools and software work and teaches in rigour the underlying concepts and algorithms from matrix theory. So any work which is congruent with (or builds up on) this field can benefit from the understanding of this course.

Reviewed by Anand Kalvit anandiitb12@gmail.com