TEW - Linear Algebra with applications to data analysis and control (2019)

Speakers and Syllabus

Objectives of the workshop :- With exponential growth of computing power and availability of historical data records in digital form is rapidly transforming industrial production systems. As a consequence, applied mathematics and computations have assumed significant importance in design and operation of engineered systems. Linear Algebra and its applications arguably assume a central position in engineering mathematics. While linear algebra related courses are taught in the first year of engineering, students often fail to grasp importance and relevance of this important tool. Thus, it is important to teach linear algebra with “engineering flavour” to students pursuing under-graduate and post-graduate studies engineering. Providing exposure to different engineering applications when various linear algebra tools are taught can help in assimilating ideas better and significantly enhance the learning experience.This course is aimed at teaching various linear algebra techniques with a strong emphasis on engineering applications. The course material will connect important concepts in linear algebra with real world engineering applications, which can be used to motivate UG and PG students.

Syllabus for the lecture series

Name of the speakers with affiliation Topic Detailed syllabus
Harish Pillai
EE Department, IIT Bombay
Solutions of Systems of linear equations

Linear systems and their solutions -- when does a solution exist, how accurate is the solution, how to solve the equations while minimising the error, how to estimate whether the solution obtained is close to the "real" solution. In the process, I would touch on condition number of a matrix, Givens rotations, Householder transforms, LU decomposition.

Sudhir R. Ghorpade
Mathematics Department, IIT Bombay
Applications of linear algebra to differential equations

We will begin with a quick review of basics of systems of linear equations and the notions of eigenvalues, eigenvectors and diagonalization of matrices. Then we consider systems of the first order linear differential equations and outline how the methods of linear algebra can be applied to the problem of determining their solutions. We shall also see how this relates to solving homogeneous linear differential equations of nth order. Applications to electrical networks may also be indicated.

J. K. Verma
Mathematics Department, IIT Bombay
Singular Value decomposition of rectangular matrices

The singular value decomposition is closely associated with the eigenvalue-eigenvector decomposition of symmetric matrices. It applies to any rectangular matrices. It has numerous applications. We shall discuss applications to the least squares problem and polar decomposition of matrices.

Vikram Gadre
Electrical Engineering Department, IIT Bombay
Transforms in image and signal processing

Introducing Transforms: Fourier Transform, Wavelet Transform, Radon Transform and generalising to multiple dimensions. Connecting transforms to linear algebra principles and illustration with examples. Mathematical principles of filtering: examples of signal and image filters.

S. A. Soman
Electrical Engineering Department, IIT Bombay
Least squares approximations and power systems

Solving Large and Spare Linear Least Squares Problem with Applications to Power System State Estimation. We will explore the following. Overview of Overdetermined Full Rank Linear Least Squares problem. Solving it using normal equations approach and QR decomposition. Sparsity issues and reduction of fill ins during LDU & QR factorisation. Formulation of power system state estimation problem as LSE problem.

Sachin Patwardhan,
Chemical Engineering Department, IIT Bombay
Applications of singular and eigenvalues

Module 1

(Applications of Singular Value Decomposition for Big-Data Analysis) Fault (abnormal behaviour) detection and diagnosis using Principle component analysis (PCA), Fault diagnosis using Fisher Discriminant Analysis, Soft sensor development using Partial Least Squares (PLS), time series modelling using Dynamic PCA.

Module 2

(Applications of Eigenvalue based Analysis for Design and Control) Analysis of local stability of engineered systems using local linearisation and eigenvalue based analysis, linear feedback controller synthesis using eigenvalue assignment, convergence of numerical schemes for solving linear algebraic equations using eigenvalue based analysis

Time Table

18 Nov
19 Nov
20 Nov
21 Nov
22 Nov
23 Nov
9.30-11.00 Pillai Pillai Verma Verma Soman Soman
11.00-11.15 Tea     
11.15-12.45 Ghorpade Ghorpade Gadre Gadre Patwardhan Patwardhan
1.00-2.30 Lunch
Lab session
Pillai Belur
Sudarshan Aditya
Ghorpade Gopi
Rekha Ruma
Verma Belur
Sudarshan Aditya
Gadre Venkitesh
Kriti Hiranya
Patwardhan Venkitesh
Kriti Hiranya
Soman Gopi
Rekha Ruma
4.30-5.00 Tea
5.00-6.00 Bapat* Belur Karamchandani Borkar Netrapalli Deshpande
* To be confirmed

 Lab Instructors

Name Affiliation Topics Dates of
the Lab
Prof. Madhu Belur
P. Sudrshan
Aditya Nadkarni
EE Department, IIT Bombay 1. Linear equations
2. Singular Value decomposition
18 Nov
20 Nov
Venkitesh Iyer
Kriti Goel
Hiranya Kishore Dey
Mathematics Department, IIT Bombay 1. Transforms in image and signal processing
2. Applications of singular and eigenvalues
Gopikrishnan C. R.
Rekha Khot
Ruma Rani Maity
Mathematics Department, IIT Bombay 1. ODEs and eigenvalues
2. Least squares approximations

 Public Lectures at 5 p.m.

Speaker Affiliation
Preneeth Netrapalli Microsoft Research
Amit Deshpande Microsoft Research
Nikhil Karamchandani EE, IIT Bombay
Madhu Belur EE, IIT Bombay
Ravindra Bapat ISI, Delhi
Vivek Borkar EE, IIT Bombay
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