Seminar Details
2018-01-12 (14:00) : Inexact Linear Solves for Model Reduction
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Kapil Ahuja (IIT Indore, India)
Abstract :
Dynamical systems arise in varied fields of science and technology. Dimension of such systems is usually large. Hence, simulations using them is cumbersome. Model reduction of a large dynamical system gives us a smaller dynamical system that mimics the input-output behavior of the original dynamical system.
With the increase in the dimension of the original dynamical system, the model reduction process itself becomes a hard task. The reason behind this is that most model reduction algorithms require solution of linear systems of equations, which traditionally are solved by direct methods that scale badly with increase in the dimension. This is the main motivation for using iterative methods for solution of linear systems of equations arising in model reduction algorithms.
Iterative methods are inexact in nature. That is, they solve a linear system up to a certain tolerance. Hence, studying stability of model reduction algorithms with respect to the error introduced by inexact solves is an important task. In this talk, I will discuss this kind of backward stability of popular model reduction algorithms for first-order bilinear and second-order linear dynamical systems.