Numerical Linear Algebra
January- April 2017

Lectures:	Monday and Wednesday from 10:30 to 11:45
Classroom:	Lecture Hall 4
Instructor:	Kavita Sutar-Deshpande
Contact:	Office: 405
	phone: 963
	email: ksutar AT cmi DOT ac DOT in
Texts:	Numerical Linear Algebra by Lloyd N. Trefethen and David Bau III, SIAM. Reference books: Introduction To Numerical Linear Algebra And Optimisation by P.G. Ciarlet. Applied numerical linear algebra by James Demmel. Introduction to Linear Algebra by Gilbert Strang.
Teaching Assistant:	Sumegha Premchandar email: sumegha AT cmi DOT ac DOT in
Grading:	25 % - Mid-semester exam 30 % - Final exam 25 % - Homework 15 % - Project and presentation 5 % - Instructor's discretion (based on participation in the course) All grades will be uploaded on Moodle.

Course syllabus

Review of linear algebra (vector spaces, linear maps, matrix of a linear transformation, effect of change of basis, Hermitian, normal and unitary matrices, inner product and norms, eigenvalues and eigenvectors, diagonalisable matrices, Jordan normal form, other reductions of matrices, singular values).
Matrix norms, Rayleigh quotient.
Introduction to conditioning and stability.
Gaussian elimination, LU decomposition, Cholesky factorisation (algorithms, operation counts, conditioning and stability issues for these methods).
Least squares problems.
QR factorization, Gram-Schmidt orthogonalisation, Householder's method.
The singular value decomposition and its applications
Iterative methods for solving linear systems: the method of conjugate gradients, Gauss-Seidel, successive over-relaxation.
Eigenvalue problems.
Using scilab.

Course components

The course will consist of in-class lectures during all weeks of the semester. Homework will be assigned every week (barring only exam weeks). Students will work in groups on a project during the semester and presentations will be in April. There will be a midterm exam in February and a final exam at the end of the semester.

Homework

Homework will be posted on this website every Sunday night and will be due in one week (on the following Monday).

Late submissions will carry penalties.
You may work alone or in groups to do your homework. In any case, you must write your own solutions.

Attendance

Attendance to classes is not required but absences will be noted. Explanation for longer absences (more than one class) is required.

Project

Your project should be connected to numerical linear algebra. It can be either Scilab or Python based. In your proposal, you should outline the importance of your project and its feasibility.
There should also be a survey of the literature related to your project. The project and presentation schedule will be as follows:

Monday, January 23: submit project proposal.
Monday, February 13 : progress report 1.
Monday, March 13: progress report 2.
(dates TBA): project presentations.
Saturday, April 15: project submission.

All submissions must be typeset in LaTeX. Each group will get 30 minutes for the presentation. Ideally, a presentation should include a description of your problem, your study, the present state of the problem, an example and a conclusion. Each member of the group should be actively involved in the presentation. Please allow 5 minutes of your time for possible questions from the audience.

Warning against copying/plagiarism

Please be warned that I will not tolerate any kind of plagiarism in your work. You are free to search for ideas on the internet and in books but the details and work have to be your own.

According to the Merriam-Webster OnLine Dictionary, to plagiarize means:

to steal and pass off (the ideas or words of another) as one's own
to use (another's production) without crediting the source;
to commit literary theft;
to present as new and original an idea or product derived from an existing source.

Synonyms: copying, appropriation, infringement, piracy, counterfeiting, theft, borrowing.

Please visit www.plagiarism.org for more details.

Schedule

Week	Topic
1 (02/01 - 06/01)	Review of linear algebra; orthogonal vectors and matrices (TB: Chap. 1, Lecture 2). Homework 1 (due on 09/01)
2 (09/01 - 13/01)	Matrix norms; Rayleigh quotient. Homework 2 (due on 18/01)
3 (16/01 - 20/01)	Singular value decomposition. Homework 3 (due on 23/01)
4 (23/01 - 27/01)	Gaussian elimination, LU factorization; partial and complete pivoting; algorithms for GE; operation count. Homework 4 (due on 30/01) Project proposal (due on 23/01)
5 (30/01 - 03/02)
6 (06/02 - 10/02)	Floating point arithmetic, conditioning and stability. Homework 5 (due on 17/02)
7 (13/02 - 17/02)	Project report 1 (due on 13/01)
8 (20/02 - 24/02)	Mid-semester exams week.
9 (27/02 - 03/03)	Iterative methods for solving a system of linear equations. Homework 6
10
11
12
13
14
15
16
17 (24/04 - 28/04)	Final exams week.

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Numerical Linear Algebra January- April 2017

Homework

Numerical Linear Algebra
January- April 2017