Polynomial acceleration of iterative schemes associated with subproper splittings

摘要

A subproper splitting of a matrix A is a decomposition A = B − C such that the kernel of A includes that of B while the range of B includes that of A. Our purpose in the present work is to extend the convergence analysis of polynomial acceleration to the case of iterative schemes associated with subproper splittings, in the case of Hermitian matrices and consistent systems. Briefly stated, our conclusions show that the regular theory extends to the subproper case provided that “convergence to the solution of Ax = b” is understood as “convergence to a solution of Ax = b ” while σ(B −1 A) is understood as σ(B+ A)\{0} where B+ is the Moore-Penrose inverse of B.