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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., Comment: 32 pages, LaTeX2e, 0 figures

With the rapid development of freight industry in our country and foreign logistics giants to enter, freight market is more and more fierce, in order to achieve the power-and-power union, many shipping companies begin to choose to form a union of carriage of goods, and whether cargo transport union will form and form a stable operation is the key of the cargo transport business decisions, based on the enterprise facing this problem, this article uses the method of shapley values proves that the various types of cargo transportation enterprise in the alliance's expected return is greater than the expected return and not joint or part of a joint interest distribution of game analysis model is set up, for the enterprise to form a coalition to provide the theoretical basis of allocation negotiation.

In this paper, the confluent form of the multistep e-algorithm is proposed. The molecule solution of this system is derived by using determinantal identities. A new continuous prediction algorithm based on this confluent form is constructed. It also shows that this algorithm is a special case of the extended Lotka‐Volterra system.

In this paper, a generalization of the G-transformation is proposed together with the corresponding auxiliary rs-algorithm for implementation. We show that the related generalization of the rs-algorithm is equivalent to a generalized qd-algorithm. Applications of the generalization of the G-transformation to the computation of infinite integrals are also given.

This paper is motivated by some recent work of Fukuda, Ishiwata, Iwasaki, and Nakamura (Inverse Problems 2009; 25:015007). We first design an algorithm for computing the eigenvalues of a specially structured matrix from the discrete Bogoyavlensky Lattice 2 (dBL2) system. A Lax representation for the dBL2 system is given in a matrix form. By considering the asymptotic behavior of dBL2 variables, some characteristic polynomials are then factorized. A new algorithm for computing the complex eigenvalues of a specially structured matrix is then introduced. Copyright © 2010 John Wiley & Sons, Ltd.

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., Comment: 12 pages, LaTeX2e, 0 figures, SIAM Journal on Scientific Computing, in press

A q-difference lattice Boussinesq equation and its confluent form are proposed. With the help of determinant identity, their molecule solutions are constructed. It is shown that the q-difference lattice Boussinesq equation can be used as a numerical convergence acceleration algorithm to compute the approximation limt → ∞f(t). Numerical examples with the application of this algorithm are presented.

In this paper, we present the cross rules of some extrapolation algorithms. These new cross rules are similar in their spirit to the cross rule for the scalar e-algorithm and the -algorithm. The first interest of such rules is that, in the algorithms for implementing sequence transformations for the acceleration of the convergence, they allow us to compute only the quantities which have a signification for extrapolation and to jump over the intermediate ones. The second interest comes out from the link between convergence acceleration methods, soliton theory and discrete integrable systems. In some cases, cross rules directly lead to physically significant integrable systems. For example, the cross rule of the confluent qd-algorithm leads to the celebrated Toda equation, which is known to have physical applications.