Structured generalized eigenvalue condition numbers for parameterized quasiseparable matrices

Abstract(#br)In this paper, when A and B are {1;1}-quasiseparable matrices, we consider the structured generalized relative eigenvalue condition numbers of the pair $$(A, \, B)$$ ( A , B ) with respect to relative perturbations of the parameters defining A and B in the quasiseparable and the Givens-vector representations of these matrices. A general expression is derived for the condition number of the generalized eigenvalue problems of the pair $$(A,\, B)$$ ( A , B ) , where A and B are any differentiable function of a vector of parameters with respect to perturbations of such parameters. Moreover, the explicit expressions of the corresponding structured condition numbers with respect to the quasiseparable and Givens-vector..