Convergence of intermediate rows of minimal polynomial and reduced rank extrapolation tables

Let {x _m} _m ^=0/ be a vector sequence obtained from a linear fixed point iterative technique in a general inner product space. In two previous papers 6,9] the convergence properties of the minimal polynomial and reduced rank extrapolation methods, as they are applied to the vector sequence above, were analyzed. In particular, asymptotically optimal convergence results pertaining to some of the rows of the tables associated with these two methods were obtained. In the present work we continue this analysis and provide analogous results for the remaining (intermediate) rows of these tables. In particular, when {x _m} _m ^=0/ is a convergent sequence, the main result of this paper says, roughly speaking, that all of the rows converge, and it also gives the rate of convergence for each row. The results are demonstrated numerically through an example.