Abstract: Early in our school days we learn curve-fitting. We are told to note down a few readings from an instrument - call it pressure and temperature – and based on à priori knowledge of the physics of the process being studied, we are asked to fit a straight line through these points, and we call it the "least-squares" fit. This line enables us to read pressure at any arbitrary temperature. Little do we realize then that this simple technique has larger ramifications in the world of engineering. To name a few, the Fourier series in signal processing, the Kalman filter in estimation, the assumed-modes model in structures. I shall start with an initial exposition to a mathematical structure called a vector space, the notion of a basis, an inner product, and how these lead to the concept of a projection, and then the classical least-squares problem viewed as a projection on a subspace. I shall then move on to other applications like the Fourier series and the Kalman filter.
Speaker Profile : Ravi Banavar is a professor at the Systems and Control Engineering, IIT Bombay (and currently a Guest Professor, IIT Gandhinagar). His current research spans the areas of 1) geometric control laws in a coordinate-free setting for constrained mechanical systems and a network of agents, (2) computing explicit bounds in the inverse function theorem and the implicit function theorem, and exploring applications that benefit from these, (3) exploring various facets of the discrete time Maximum Principle, with particular emphasis on frequency constraints, rate constraints and numerical techniques to solve two-point boundary value problems, (4) estimation algorithms on Lie groups - theory and computation. He obtained a PhD from University of Texas at Austin and has a BTech from Indian Institute of Technology, Madras.
January
2 0 2 6
12
Monday
4:00 PM – 5:00 PM IST
SPEAKER
Ravi Banavar
Professor
IIT Bombay
The Least-Squares Problem in Engineering
Expert Talk Series
School of Engineering and Applied Science
Room 100, First Floor
GICT Building, Central Campus
This talk is organised by School of Engineering and Applied Science, Ahmedabad University