Ghosh, Arnab2019-07-082023-10-262019-07-082023-10-262017ROLL NO.09612307https://gyan.iitg.ac.in/handle/123456789/1091Supervisor: Rafikul AlamWe develop a general framework for the sensitivity and backward perturbation analysis of linear and polynomial MEPs. For a general norm on the space of MEPs, we define the condition number cond( ,W) of a simple eigenvalue of an MEPWand derive three equivalent representations of cond( ,W).We also analyze holomorphic perturbation of a simple eigenvalue of W. Further, we define the backward error ( ,W) of an approximate eigenvalue of W. We determine ( ,W) and construct an optimal perturbation W such that 2 (W+ W) and ||| W||| = ( ,W). We also define the backward error ( , x,W) of an approximate eigenpair ( , x := x1 · · · xm) 2 Cm × (Cn1 · · · Cnm). We determine ( , x,W) and construct an optimal perturbation W such that W( )x + W( )x = 0 and ||| W||| = ( , x,W). We define and analyze two vector spaces, namely, the right ansatz space and the left ansatz space of potential linearizations of a two-parameter matrix polynomial of the form P( , μ) := Pk i=0 Pk−i j=0 iμjAij . We also analyze conditions under which a pencil in the ansatz spaces is a linearization of P( , μ). We consider structured linear MEPs and define structured backward error S( , x,W) of an approximate eigenpair ( , x := x1 · · · xm). We determine S( , x,W) and construct an optimal structured perturbation W such that W( )x + W( )x = 0 and ||| W||| = S( , x,W).enMATHEMATICSThesis