  In this paper, we give a multistep extension of the epsilon-algorithm of
Wynn, and we show that it implements a multistep extension of the Shanks'
sequence transformation which is defined by ratios of determinants.
Reciprocally, the quantities defined in this transformation can be recursively
computed by the multistep epsilon-algorithm. The multistep epsilon-algorithm
and the multistep Shanks' transformation are related to an extended discrete
Lotka-Volterra system. These results are obtained by using the Hirota's
bilinear method, a procedure quite useful in the solution of nonlinear partial
differential and difference equations.
