Title: Structured eigenvalue problems and their applications
ABSTRACT: We discuss the structured, backward error analysis of an approximate eigenpair for Hermitian, skew-Hermitian, symmetric, and skew-symmetric matrices. We review results on minimal structured perturbation such that an estimated eigenpair becomes an exact eigenpair of an appropriately perturbed matrix. Then, we discuss on minimal structured perturbation of an approximate eigenpair that becomes a precise eigenpair of a suitably perturbed nonlinear matrix equation. Moreover, we show that our general framework generalizes the existing results in the literature on perturbation theory of a matrix polynomial. We extend perturbation analysis on the specified eigenpairs on the above-structured problems.
Dr. Ahmad was born and brought up in Bhadrak, Odisha. He did his B.Sc. from Bhadrak College and recieved his M.Sc. in Mathematics from Utkal University. Further, he received his M.Phil. from Ravenshaw University. He was awarded the Ph.D. degree in Mathematics from IIT Guwahati in 2008 with the help of GATE and SRF from CSIR. His thesis was concerned with “Pseudosepectra of Matrix pencils and their Applications in Perturbation Analysis of Eigenvalues and Eigen decompositions”. After his thesis submission he joined in SERC, IISc. Bangalore as a Research Associate in 2nd January 2008. One-year after his research at IISc, he receieved NBHM Post Doctoral fellowship funded by DAE and German Post Doctoral Fellowship BAT IIa. So he accepted German Fellowship and visited to the Institut für Mathematik, Universität Berlin, Germany in 2nd February 2009 as a Post Doctoral Fellow and then in Dec. 2009, he returned to IIT Indore and acted as an Associate Professor at the Discipline of Mathematics. His research interest lies inside Numerical Linear Algebra and the study of logarithmic norm for matrix pencils which are associated with Differential Algebraic Equations (DAE), Differential Equations (DEs), and Stochastic Differential Equations (SDEs).