Matrix extrapolation algorithms Original Research Article

Extrapolation algorithms are used for accelerating scalar or vector sequences. They are also used for solving systems of linear and nonlinear equations. These algorithms are expressed in terms of a ratio of two determinants, as the E-algorithm and the general recursive projection algorithm (image). In this paper we define the matrix extrapolation problem and we use the Schur complement and the Sylvester identity for solving this problem; we give two transformations, equivalent to the E-algorithm and the image, for the matrix case. We give also a characterization of their kernels.