SCAIM Seminar: Chen Greif (UBC)

Saddle-point linear systems arise in many applications involving problems with constraints. When the underlying matrices are large and sparse, iterative solvers are typically used. A number of Krylov subspace solvers can be used, but they do not necessarily take into account the block structure of the matrix. As a result, the underlying Lanczos process does not approximately preserve the inertia of the matrix throughout the iteration. In this unpolished talk I will describe my latest attempts to develop a solver that aims to preserve the structure and the inertia in the projected subspace. To accomplish this, a new block Arnoldi/Lanczos-type algorithm is used, and the result is an oblique projection method whose speed of convergence depends on the spectral structure of the matrix.