Block extrapolation methods with applications

In the present paper we introduce new block extrapolation methods as generalizations of the well known vector extrapolation methods. We give expressions of the obtained approximations via the Schur complement and also propose an efficient implementation of these methods. Applications to linearly generated sequences are given and extensions to nonlinear problems are also given. Applications of the proposed block extrapolation methods to some nonlinear matrix equations are considered and some numerical examples are given.