COL7(1)26: Numerical Algorithms

Course Description

Content: Number representation, fundamentals of error analysis, conditioning, stability, singular value decomposition and its applications, QR factorization, condition number, least squares and regression, Gaussian elimination, eigenvalue computations and applications, iterative methods, root finding, elements of convex optimization including steepest descent and Newton’s method.

Textbooks:

Primary references:

• Michael T. Heath, Scientific Computing: An Introductory Survey, 2nd Ed.
• Lloyd Trefethen and David Bau, Numerical Linear Algebra

Other suggested textbooks:

• Ward Cheney and David Kincaid, Numerical Mathematics and Computing
• Stephen Boyd and Lieven Vandenberghe, Convex Optimization

Prerequisites: COL106 or equivalent. Familiarity with linear algebra and calculus is assumed. You will be expected to write programs in Python or MATLAB.

Overlaps with: MTL704.

Announcements: All announcements will be made on Piazza. It is your responsibility to check it regularly.

Lectures

Lecture topics and relevant textbook chapters will be listed here as the semester proceeds.

1. 5 Jan 2026: Introduction, errors in computation, condition number (Heath 1.1–2)
2. 8 Jan 2026: Floating-point representation, machine precision, cancellation errors (H 1.3)
3. 12 Jan 2026: Accuracy and stability, review of linear algebra (Trefethen & Bau 14, 15)
   • Further reading: David Goldberg, “What every computer scientist should know about floating-point arithmetic”
4. 15 Jan 2026: Linear transformations, matrix multiplication, orthogonality (TB 1–2)
5. 19 Jan 2026: Vector and matrix norms (TB 3)
6. 22 Jan 2026: The singular value decomposition (TB 4-5)

Policies

Evaluation:

• Homeworks and quizzes: 30%
  • Homework 1
• Mid-sem exam: 30%
• End-sem exam: 40%

Students should use either Python 3 (with Numpy/Scipy) or MATLAB for the programming component of the homework. Some online tutorials and references for Numpy:

• Python Numpy Tutorial
• NumPy: the absolute basics for beginners
• NumPy Cheat Sheet

Late policy: Homework assignments are due at midnight on the due date. You are allowed a total of 4 late days across all the assignments. Any submissions exceeding these limits will not be graded.

Audit pass requirements: At least 75% attendance, 50% marks in the course total, and 20% marks in each homework, quiz, and exam.

Attendance policy: Attendance lower than 50% will result in a one-grade penalty (e.g. A to A–, or A– to B).

Academic dishonesty: Any cases of plagiarism or other unfair means will result in strict disciplinary action and referral to the CSE department’s disciplinary committee.