Yi He, Xing-Biao Hu, Jian-Qing Sun et al.
The molecule solution of an equation related to the lattice Boussinesq equation is derived with the help of determinantal identities. It is shown that this equation can for certain sequences be used as a numerical convergence acceleration algorithm. Numerical examples with applications of this algorithm are presented.
Claude Brezinski, Yi He, Xing-Biao Hu et al.
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.
Xiang-Ke Chang, Yi He, Xing-Biao Hu et al.
We construct new sequence transformations based on Wynn's epsilon and rho algorithms. The recursions of the new algorithms include the recursions of Wynn's epsilon and rho algorithm and of Osada's generalized rho algorithm as special cases. We demonstrate the performance of our algorithms numerically by applying them to some linearly and logarithmically convergent sequences as well as some divergent series.