2024-25, Sem 2
Instructor: Rajendra Kumar
Email: rajendra@cse.iitd.ac.in
Lecture Timings: Mondays and Thursdays, 9:30 AM - 11:00 AM; Venue: LH 512
Office Hours: Mondays and Thursdays, 3 PM - 4 PM and by appointment.
The final grade will be based on the following components:
Audit Policy: To audit pass this course, minimum 75% attendance and need to earn marks equivalent to a grade B- or above.
Assignments: You have a total of three late days available for all assignments combined. Submissions exceeding this limit will not be graded.
Plagiarism: Any form of plagiarism will result in strict disciplinary action.
Name: Rupesh Kumar
Email: csz228228@iitd.ac.in
Office Hours: Tuesdays, 4 PM - 5 PM
Name: Vipul Garg
Email: cs5200450@cse.iitd.ac.in
Office Hours: Mondays, 5 PM - 6 PM
Name: Shivam Jain
Email: cs5200626@cse.iitd.ac.in
Office Hours: Tuesdays, 5 PM - 6 PM
| Lecture | Date | Topic | Reference |
|---|---|---|---|
| 1 | 02 Jan 2025 | Introduction, Errors in computation, Condition number, Stability | [H] Chapter 1 |
| 2 | 06 Jan 2025 | Floating Point Representation, Machine Precision, Cancellation errors | [H] Chapter 1, 2.3.1, [TB] Chapters 12 |
| 3 | 09 Jan 2025 | linear Algebra review, Norms of vectors | [TB] Chapters 1,2,3 |
| 3 | 13 Jan 2025 | Canceled | |
| 4 | 20 Jan 2025 | Norm of a matrix, invariance of 2-norm under unitary transformation, Singular Value Decompostion | [TB] Chapter 3,4 |
| 6 | 23 Jan 2025 | Completion of the proof of the SVD theorem, low-rank approximation by SVD | [TB] Chapter 5 |
| 7 | 27 Jan 2025 | Applications of SVD, Projectors | [TB] Chapter 6 |
| 8 | 30 Jan 2025 | Least Squares, Normal Equations, Least Squares from QR factorization, Quiz I | [TB] Chapters 7, 11 |
| 9 | 03 Feb 2025 | Conditioning of Least Squares, Gram Schmidt Orthonormalization | [H] Chapter 3.2, 3.3, [TB] Chapter 8 |
| 10 | 06 Feb 2025 | Modified Gram Schmidt and stability | [TB] Chapter 8, 19 |
| 11 | 10 Feb 2025 | Householder Transformation, QR Factorization using Householder | [TB] Chapter 10 |
| 12 | 13 Feb 2025 | Gaussian Elimination, LU Factorization, Partial Pivoting | [TB] Chapters 20, 21,22 |
| 13 | 17 Feb 2025 | Cholesky Decomposition | [TB] Chapter 23 |
| 14 | 20 Feb 2025 | Eigenvalues and some applications | [TB] Chapter 25 |
| 15 | 03 Mar 2025 | Schur Factorization, Power Iteration | [TB] Chapters 24, 27 |
| 16 | 06 Mar 2025 | Inverse Iteration, Rayleigh Quotient, Inverse Iteration with Shifts | [TB] Chapter 27 |
| 17 | 17 Mar 2025 | Iterative Methods for Linear Systems: Jacobi Method, Gauss-Seidel Method | [H] Chapter 11.5 |
| 18 | 20 Mar 2025 | Krylov Space, Arnoldi Iteration | [TB] Chapters 33, 34 |
| 19 | 24 Mar 2025 | Arnoldi Iteration and Eigenvalue computation | [TB] Chapters 33, 34 |
| 20 | 27 Mar 2025 | Non-linear Equations; bisection method, fixed point iteration convergence, , Quiz II | [H] Chapter 5 |
| 20 | 28 Mar 2025 | Quiz II, 6:45PM to 8:15PM | LH108 |
| 21 | 03 Apr 2025 | Non-linear Equations: Newton's method, Secant method, convergence | [H] Chapter 5 |
| 22 | 07 Apr 2025 | Non-linear Equations: Newton's method in Higher Dimensions, Broyden's method, | [H] Chapter 5 |
| 23 | 12 Apr 2025 | Optimization, Convex functions in higher dimensions and their properties | [BV] Chapter 1.1-1.3,2.1-2.3,3.1-3.3 |
| 24 | 14 Apr 2025 | Holiday | |
| 25 | 17 Apr 2025 | Unconstrained Optimization: Gradient Descent, Quiz III 6:45-8:00 PM | [BV] Chapter 9 |
| 26 | 21 Apr 2025 | Steepest Descent Method, Newton's Method and Convergence | [BV] Chapter 9 |
| 27 | 24 Apr 2025 | ||
| 28 | 28 Apr 2025 |