Numerical Algorithms and Tensor Learning Laboratory

Ratikanta Behera

Teaching

IISc Bangalore, India

Indian Institute of Science • 2022 - Present
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  • DS 288/UMC 202 Numerical Methods

    Fall 2025

    DS 288 / UMC 202

    Numerical Methods (Fall 2025)

    Course Outline
    Numerical methods are routinely used in all disciplines of science and engineering, which serve as the approximate solutions to real-time problems. This course will cover the formulation/mathematics behind the contemporary numerical methods, which later will be applied to solving the example real world problems. The emphasis of the course will be more on the deep understanding of these numerical methods, with homework geared towards application and analysis of this.
    Topics Covered
    • Introduction & Motivation (Types of error in numerical computation)
    • Multivariable calculus and its applications
    • Solutions of Equations of One Variable
    • Interpolation and Polynomial Approximation
    • Approximation Theory
    • Numerical Integration and Differentiation
    • Initial-Value Problems for ODEs
    • Solutions of Nonlinear Systems of Equations
    • Boundary-Value Problems for ODEs
    References

    Primary Reference:

    • Richard L. Burden and J. Douglas Faires, Numerical Analysis (9th edition)

    Supplemental References:

    • Kendall Atkinson, and Weimin Han, Elementary Numerical Analysis (Third Edition)
    • John H. Mathews & Kurtis D. Fink, Numerical Methods Using MATLAB, Prentice Hall
    Marking Scheme
    • Homework/Quizzes - 30% (10+10+10)
    • Midterm Exam - 20%
    • Project - 20%
    • Final Exam - 30%
    Course Links
    MS Teams Link
    SAP Link

  • DS 285 Tensor Computations for Data Science

    Spring 2025

    DS 285

    Tensor Computations for Data Science (January 2025)

    Course Outline
    This course is an introduction to tensor computations, focusing on theory, algorithms, and applications of tensor decompositions to data sciences. In the era of BIG data, artificial intelligence, and machine learning, we are faced with the need to process multiway (tensor-shaped) data. These data are mostly in the three or higher order dimensions, whose orders of magnitude can reach billions.
    Topics Covered
    • Fundamentals: Basic concepts of matrix properties: norms, rank, trace, inner products, Kronecker product
    • Introduction to Tensors: Tensors and tensor operations: Mode-n product of a tensor
    • Tensor Decomposition: Block tensor decomposition, Canonical Polyadic (CP) decomposition, the Tucker decomposition
    • Applications: Low-rank tensor approximation, background removal with robust principal tensor component analysis
    • Deep Neural Networks: Deep neural networks, Tensor networks, and their decompositions
    References
    • Liu, Y. (Ed.). Tensors for Data Processing: Theory, Methods, and Applications. Academic Press. (2021)
    • Liu Y, Liu J, Long Z, Zhu C. Tensor Computation for Data Analysis. Springer; 2022
    • T. G. Kolda and B. W. Bader. Tensor decompositions and applications. SIAM Rev., 51(3):455-500, 2009
    Marking Scheme
    • Assignments/Quizzes/Homework/Presentation - 50%
    • Midterm Exam - 10%
    • Final Exam - 20%
    • Final Project - 20%
    Course Resources
    MS Teams Link
    SAP Link
    Lecture-1 Notes

  • UE 201 Introduction to Scientific Computing

    Fall 2023