Eigenvalue problems with a double spectrum or spectrum closed under negation
Hakim Ikramov
Abstract: Eigenvalue problems with specially structured matrices often have certain pecularities in their spectrum, such as a double spectrum or spectrum symmetric with respect to zero or one of coordinate axes. The most known example of such problems concerns skew-symmetric matrices; the other examples are Hamiltonian and skew-Hamiltonian matrices, block quaternions, skew pseudoeuclidean and persymmetric matrices, their squares, and so on. In the talk, we discuss various approaches to numerical solution of problems of this kind that use known a fortiori features of their spectrum. Unfortunately, most of these approaches are numerically unstable. To make them stable is a worthy challenge for experts in numerical linear algebra.