Numerical Algorithms

This is the course page for Numerical Algorithms (COL726), for Semester II, 2016-2017, being taught by Subhashis Banerjee at the Department of Computer Science and Engineering, IIT, New Delhi.

General Information | Notices | Tutorials | Assignments | Examinations | Resources (available only from within IITD)|

General Information

Primary references:

• What Every Computer Scientist Should Know About Floating-Point Arithmetic by David Goldberg
• Elementary Numerical Analysis by Samuel Conte and Carl De Boor
• Linear Algebra by Kenneth Hoffman and Ray Kunze
• Numerical Linear Algebra by Lloyd N. Trefethen and David Bau III
• Matrix Computations by Gene H. Golub and Charles F. Van Loan

Other references:

• Answer from the master himself to the question raised in the class on whether all linear spaces are inner product spaces?
• Check out Abhiram Ranade's tutorial on Some uses of spectral methods in Computer Science (applications of SVD).
• Check out the Resources directory (updated with a tute on Gauss-Newton and SVD approximation via random sampling; available only from within IITD)

Evaluations

COL726 will have the following weightages: Minor I - 20%, Minor II - 20%, Major - 30%, Class participation - 5%, Assignments and special problems - 25%

Honour code

• All students are expected to follow the highest ethical standards.
• Collaborations and discussions are encouraged. However, all students are required to write up all solutions entirely on their own. Any collaboration, or help taken, must be declared.
• Students are encouraged to refer to books, papers and internet resources. They may even consult other individuals. However, the source must be clearly cited if any part of the solution (or even an idea) is taken from such a source.
• Failure to declare any help taken will be interpreted as academic misconduct.

Notices

1. Minor 2 take home

1. Problem set #1: Numerical computations - pitfalls. PDF.
2. Problem set #2: To err is human and to blame it on a computer is more like it. PDF.
3. Problem set #3: Polynomials. PDF.
4. Problem set #4: Some basic linear algebra. PDF.
5. Problem set #5: SVD, least squares, orthogonal projections. PDF.
6. Problem set #6: Block matrix computations. PDF.
7. Problem set #7: Error analysis of LU and some extensions. PDF.
8. Problem set #8: Householder and Givens. PDF.
9. Problem set #9: Eigenvalue and SVD computation. PDF.
10. Problem set #10: Steepest descent and conjugate gradients. PDF.

1. Do the computational problems of the first tutorials. Submit a a report containing your experiments and observations. Last date for submission is Jan 13. Please submit on Moodle.
2. Carry out numerical experiments with the problems 5 and 6 of Minor 1 and submit your observations. Last date for submission in Feb 24. Please submit on Moodle.
3. Assignment #2: SVD applications: LSI and PCA. Last date for submission is is April 20. PDF.
4. Assignment #3: Eigenvalue and SVD computation: Experiment with the methods of Tutorial 9 and SVD computation and submit a report. Last date for submission in Moodle is April 20.
5. You may submit any other interesting experiments that you may done after the majors. The link will be up here soon.