Invited Speaker
Manjunatha Prasad Karantha
-
Professor of Centre for Advanced Research in Applied Mathematics and Statistics, Department of Data Science, Manipal Academy of Higher Education, Manipal, India
-
Research interests: theory and applications of matrices and generalized inverses, matrices and graphs, nonnegative matrices, covariance matrix and its applications, ring theory, regular elements in rings and semigroup, partial order on matrices and regular elements
-
Web page: https://manipal.edu/psph/department-faculty/faculty-list/k-manjunatha-prasad.html
- Talk title: Computation of Generalized Inverses associated with Networks
Computation of Generalized Inverses associated with Networks
The topics of generalized inverses and graph theory are interconnected, rapidly advancing,
and extensively studied due to their wide applications in various branches of pure and applied science.
The generalized inverses of matrices associated with networks play a prominent role in the study of network flow,
electrical networks, defining new distances on graphs and Markov process. For example,
if Q is the incidence matrix of given network (multi-digraph) then Qx = b represent net inflow at each
vertices when the flows through the edges of network is given by x. As the matrix Q is not invertible
and the linear system Qx =b need not be consistent or with infinitely many solutions, it is of natural interest
that to find minimum inflow through n arcs of the network to achieve net inflow at m vertices
are as close as possible to the desired. Noting that such a solution is given with the help
of Moore-Penrose inverse, in this talk, we present several expressions for Q† and L†,
which are computationally simpler by using network properties and different matrix methods.
The methods include bordering, projectors, partition, and inverse complemented matrix method.
We also consider some special cases of networks such as tree graph, complete graph, and complete bipartite graph for our discussion.
The content of this talk is a part of joint work with Ravindra B Bapat and Umashankara Kelathaya.
|
