Speaker
Description
Linear algebraic systems in saddle point form arise in numerous applications in science and engineering. In general saddle point matrices are highly indefinite which slows down the convergence of many iterative methods, including Krylov subspace methods. By negating the second block row, symmetry of the saddle point matrix is traded for a spectrum that is contained in the right half plane. Further, the resulting matrix splits `naturally' into symmetric and skew-symmetric parts.
In this talk we will present a general analysis of the spectral properties of the modified saddle point matrix, derive sufficient conditions under which it is diagonalizable and has a real and positive spectrum and explain how an inner product in which the modified saddle point matrix is selfadjoint can be constructed.
This is joint work with Jörg Liesen (TU Berlin).
