COL726: Numerical Algorithms

2024-25, Sem 2

Course Instructor

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.

Course Policy

The final grade will be based on the following components:

  • 2 Assignments: 10%
  • 3 Quizzes: 15%
  • Minor Exam: 30%
  • Major Exam: 40%
  • Attendance: 5% marks for attending at least 75% of classes; otherwise, 0.

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.

References Textbooks

Teaching Assistants

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

Tentative Class Schedule

Lecture Date Topic Reference
102 Jan 2025Introduction, Errors in computation, Condition number, Stability[H] Chapter 1
206 Jan 2025Floating Point Representation, Machine Precision, Cancellation errors [H] Chapter 1, 2.3.1, [TB] Chapters 12
309 Jan 2025linear Algebra review, Norms of vectors[TB] Chapters 1,2,3
313 Jan 2025Canceled
420 Jan 2025Norm of a matrix, invariance of 2-norm under unitary transformation, Singular Value Decompostion[TB] Chapter 3,4
623 Jan 2025Completion of the proof of the SVD theorem, low-rank approximation by SVD[TB] Chapter 5
727 Jan 2025Applications of SVD, Projectors[TB] Chapter 6
830 Jan 2025Least Squares, Normal Equations, Least Squares from QR factorization, Quiz I[TB] Chapters 7, 11
903 Feb 2025Conditioning of Least Squares, Gram Schmidt Orthonormalization[H] Chapter 3.2, 3.3, [TB] Chapter 8
1006 Feb 2025Modified Gram Schmidt and stability[TB] Chapter 8, 19
1110 Feb 2025Householder Transformation, QR Factorization using Householder[TB] Chapter 10
1213 Feb 2025Gaussian Elimination, LU Factorization, Partial Pivoting[TB] Chapters 20, 21
1317 Feb 2025Cholesky Decomposition[TB] Chapter 22
1420 Feb 2025Eigenvalues and some applications[TB] Chapter 25
1503 Mar 2025Schur Factorization, Power Iteration[TB] Chapters 24, 27
1606 Mar 2025Inverse Iteration, Rayleigh Quotient, Inverse Iteration with Shifts[TB] Chapter 27
1717 Mar 2025Krylov Spaces, Arnoldi Iteration[TB] Chapters 33, 34
1820 Mar 2025Arnoldi Iteration, Quiz II[TB] Chapters 33, 34
1924 Mar 2025Arnoldi Iteration and Eigenvalue computation[TB] Chapters 33, 34
2027 Mar 2025Non-linear Equations; bisection method, fixed point iteration convergence[H] Chapter 5
2103 Apr 2025Non-linear Equations: Newton's method, Secant method, convergence[H] Chapter 5
2207 Apr 2025Non-linear Equations: Newton's method in Higher Dimensions, Broyden's method, Optimization and convex functions[H] Chapter 6
2312 Apr 2025Convex functions in higher dimensions and their properties[H] Chapter 6
2414 Apr 2025Unconstrained Optimization: Gradient Descent, Newton's method[H] Chapter 6
2517 Apr 2025ODE: First order ODE, Euler's method, Quiz III[H] Chapter 9.2, 9.3.1
2621 Apr 2025ODE: Local error and accuracy, stability, Taylor Series method, Runge Kutta Methods[H] Chapter 9.3.2, 9.3.3, 9.3.5, 9.3.6
2724 Apr 2025ODE: Multi-step methods[H] Chapter 9.3.8
2828 Apr 2025