Reduced Rank Extrapolation (RRE) is a polynomial type method used to accelerate the convergence of sequences of vectors $\{\xx_m\}$. It is applied successfully in different disciplines of science and engineering in the solution of large and sparse systems of linear and nonlinear equations of very large dimension. If $\sss$ is the solution to the system of equations $\xx=\ff(\xx)$, first, a vector sequence $\{\xx_m\}$ is generated via the fixed-point iterative scheme $\xx_{m+1}=\ff(\xx_m)$, $m=0,1,\ldots,$ and next, RRE is applied to this sequence to accelerate its convergence. RRE produces approximations $\sss_{n,k}$ to $\sss$ that are of the form $\sss_{n,k}=\sum^k_{i=0}\gamma_i\xx_{n+i}$ for some scalars $\gamma_i$ depending (nonlinearly) on $\xx_n, \xx_{n+1},\ldots,\xx_{n+k+1}$ and satisfying $\sum^k_{i=0}\gamma_i=1$. The convergence properties of RRE when applied in conjunction with linear $\ff(\xx)$ have been analyzed in different publications. In this work, we discuss the converg 查看全文>>