Discrete krylov subspace methods for equations of the second kind

Abstract

When applied to equations of the type (I+K)u = f in Hilbert spaces, where K is a compact linear operator, Krylov subspace methods possess nice convergence properties. We show that these properties are retained even when approximate problems are considered. Furthermore acceleration strategies are proposed and discussed.

Keywords:

• Krylov subspace methods
• GMRES
• FOM
• preconditioning
• Hilbert space

C.R. Categories:

• G.1.3