In this article we introduce new bounds for the condition numbers of deflated symmetric positive definite systems, used with and without classical preconditioning. For the case of a subdomain deflation such as that of Nicolaides (1987), these lemmas can provide direction in choosing a proper decomposition into subdomains and a proper choice of classical preconditioner. If grid refinement is done keeping the subdomain resolutions fixed, the condition number can be shown to be independent of the number of subdomains.

Iterative methods for linear systems (msc 65F10), Sparse matrices (msc 65F50), Solution of discretized equations (msc 65N22)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Frank, J.E, & Vuik, C. (2000). On the construction of deflation-based preconditioners. Modelling, Analysis and Simulation [MAS]. CWI.