Numerical Linear Algebra Course | IIT Dhanbad | Prof. Srinivasa Rao Pentyala
Course Details
| Exam Registration | 19 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| Credit Points | 3 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 26 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlock the Power of Computation: A Deep Dive into Numerical Linear Algebra
In the digital age, where data drives innovation, the ability to solve complex linear systems efficiently and accurately is a superpower. From the algorithms behind search engines and image recognition to simulations in aerospace engineering and financial modeling, Numerical Linear Algebra forms the bedrock of scientific computing and modern technology. This 12-week course, meticulously designed and taught by Prof. Srinivasa Rao Pentyala of IIT (ISM) Dhanbad, offers a rigorous journey into this critical field.
Why This Course is Essential for Your Career
Numerical Linear Algebra is not just an abstract mathematical discipline; it's a toolkit for solving real-world problems. This course bridges the gap between theoretical linear algebra and its practical, computational implementation. You will move beyond solving small systems by hand to understanding how computers handle massive, often ill-conditioned, matrices that arise in real applications. The focus on error analysis, algorithm stability, and computational efficiency (flop count) makes this knowledge highly valued in industry, particularly for roles in software development, data science, machine learning, and computational research.
Meet Your Expert Instructor: Prof. Srinivasa Rao Pentyala
Learning from an experienced academic and researcher is invaluable. Prof. Pentyala brings over two decades of expertise to this course:
- PhD from IIT Kanpur (2001) with a strong research foundation.
- Extensive teaching experience at premier institutions like BITS Pilani and IIT Dhanbad in core and advanced courses including Algorithms, Numerical Methods, and Computational Fluid Dynamics.
- Handled multiple R&D projects from DST, CSIR, UGC, and NBHM in areas like CFD and Numerical PDEs.
- Active guidance of UG/PG projects in Machine Learning, Deep Learning, and Scientific Computing, ensuring the course content is relevant to cutting-edge applications.
Detailed 12-Week Course Curriculum
The course is structured to build your knowledge from fundamental concepts to advanced applications, culminating in modern AI techniques.
| Week | Core Topics Covered |
|---|---|
| Week 1-2 | Foundations: Computational difficulties, error analysis, Gaussian Elimination, LU/QR factorization, Cholesky decomposition. |
| Week 3-4 | Matrix Decompositions & Least Squares: Projections, Householder reflectors, SVD for image compression, pseudo-inverse, eigenvalue problems. |
| Week 5-8 | Advanced Eigenvalue & SVD Algorithms: Power method, QR iteration, Jacobi method, Golub-Kahan-Reinsch SVD algorithm, Generalized SVD. |
| Week 9-11 | Iterative Methods for Large Systems: Krylov subspace methods (Lanczos, Arnoldi), convergence analysis, stability of algorithms. |
| Week 12 | AI Applications & Hands-On Session: Solving sensitive PDE systems (e.g., aerodynamics), applications in image processing using AI techniques. |
Who Should Enroll?
This course is designed as an open elective with broad appeal:
- Intended Audience: Undergraduate (UG), Postgraduate (PG), and PhD students in Computer Science (CSE), Electrical (EE), Electronics (ECE), Mathematics & Computing (M&C), and Civil Engineering (CE).
- Prerequisites: Basic knowledge of linear algebra and numerical analysis is helpful but not mandatory. The course builds concepts from the ground up.
- Industry Support: The skills taught are directly applicable in industries relying on scientific computation, simulation, data analysis, and algorithm development, enhancing placement prospects in software and R&D roles.
Key Learning Outcomes
By the end of this course, you will be able to:
- Implement and analyze key matrix factorization techniques (LU, QR, Cholesky, SVD).
- Solve least squares problems and understand sensitivity analysis using condition numbers.
- Compute eigenvalues/eigenvectors for both standard and large, sparse systems.
- Choose the appropriate iterative or direct solver for a given linear system based on its properties.
- Appreciate the application of these methods in domains like machine learning, image processing, and computational physics.
Recommended Textbooks
- B.N. Datta: Numerical Linear Algebra and Applications (SIAM, 2011).
- R.S. Varga: Matrix Iterative Analysis (Springer, 2000).
Embark on this 12-week journey to master the numerical engines that power scientific discovery and technological innovation. Enroll today and build a formidable skill set at the intersection of mathematics, computer science, and engineering.
Enroll Now →