MATRIX EXTRAPOLATION ALGORITHMS

Extrapolation algorithms are used for accelerating scalar or vector se quences. They are also used for solving systems of linear and nonlinea r equations. These algorithms are expressed in terms of a ratio of two determinants, as the E-algorithm and the general recursive projection algorithm (GRPA). In this paper we define the matrix extrapolation pr oblem and we use the Schur complement and the Sylvester identity for s olving this problem; we give two transformations, equivalent to the E- algorithm and the GRPA, for the matrix case. We give also a characteri zation of their kernels. (C) Elsevier Science Inc., 1997.