A geometric theory for preconditioned inverse iteration. I: Extrema of Rayleigh quotient (Q1595116)

The method of preconditioned inverse iteration calculates some eigenvalues of large sparse matrices arising e.g. in finite element discretization of partial differential equations. The solution of linear equations in each step of the original inverse iteration is replaced by using a preconditioner, often a multigrid preconditioner. A convergence analysis is given in Part II [ibid. 322, No. 1-3, 87-104 (2001)]. It is based on several results derived in Part I, e.g. on the maximum of the Rayleigh-quotient, if the preconditioner lies in a certain class.