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 con...
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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.
In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, a...
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In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, and Redivo-Zaglia cannot be expressed as a ratio of two determinants. Motivated by this, we will introduce a new algebraic tool-pfaffians, instead of determinants in the paper. It turns out that Brezinski-Durbin-Redivo-Zaglia's transformation can be expressed as a ratio of two pfaffians. To the best of our knowledge, this is the first time to introduce pfaffians in the expressions of sequence transformations. Furthermore, an extended transformation of high order is presented in terms of pfaffians and a new convergence acceleration algorithm for implementing the transformation is constructed. Then, the Lax pair of the recursive algorithm is obtained which implies that the algorithm is integrable. Numerical examples with applications of the algorithm are also presented.
In this paper, we show that the coupled modified Kd V equations possess rich mathematical structures and some remarkable properties. The connections between the system and skew orthogonal polynomials,convergence accel...
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In this paper, we show that the coupled modified Kd V equations possess rich mathematical structures and some remarkable properties. The connections between the system and skew orthogonal polynomials,convergence acceleration algorithms and Laurent property are discussed in detail.
This paper presents an iterative scheme for the solution of the large matrix equations arising in the full-wave electromagnetic analysis of printed antenna arrays. The proposed technique is based on the Jacobi decompo...
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This paper presents an iterative scheme for the solution of the large matrix equations arising in the full-wave electromagnetic analysis of printed antenna arrays. The proposed technique is based on the Jacobi decomposition of a matrix linear equation which allows the construction of an iterative solution scheme. It is demonstrated that the coupling of the iterative process to a convergence accelerator algorithm guarantees convergence, even when ill-conditioned problems are treated. Numerical implementation is discussed, and the advantages of the proposed technique are illustrated through the analysis of a practical slot feed patch away. (C) 1997 John Wiley & Sons, Inc.
In this paper, we propose a generalized discrete Lotka-Volterra equation and explore its connections with symmetric orthogonal polynomials, Hankel determinants and convergence acceleration algorithms. Firstly, we exte...
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In this paper, we propose a generalized discrete Lotka-Volterra equation and explore its connections with symmetric orthogonal polynomials, Hankel determinants and convergence acceleration algorithms. Firstly, we extend the fully discrete Lotka-Volterra equation to a generalized one with a sequence of given constants {u(0)((n))} and derive its solution in terms of Hankel determinants. Then, it is shown that the discrete equation of motion is transformed into a discrete Riccati system for a discrete Stieltjes function, hence leading to a complete linearization. Besides, we obtain its Lax pair in terms of symmetric orthogonal polynomials by generalizing the Christoffel transformation for the symmetric orthogonal polynomials. Moreover, a generalization of the famous Wynn's c-algorithm is also derived via a Miura transformation to the generalized discrete Lotka-Volterra equation. Finally, the numerical effects of this generalized c-algorithm are discussed by applying to some linearly, logarithmically convergent sequences and some divergent series.
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 generali...
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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.
作者：
Brezinski, ClaudeHe, YiHu, Xing-BiaoRedivo-Zaglia, MichelaSun, Jian-QingLaboratoire Paul Painlevé
UMR CNRS 8524 UFR de Mathématiques Pures et Appliquées Université des Sciences et Technologies de Lille France LSEC
Institute of Computational Mathematics and Scientific Engineering Computing AMSS Chinese Academy of Sciences and Graduate School of the Chinese Academy of Sciences Beijing People’s Republic of China LSEC
Institute of Computational Mathematics and Scientific Engineering Computing AMSS Chinese Academy of Sciences Beijing People’s Republic of China Università degli Studi di Padova
Dipartimento di Matematica Pura ed Applicata Italy
Abstract: In this paper, we propose a multistep extension of the Shanks sequence transformation. It is defined as a ratio of determinants. Then, we show that this transformation can be recursively implemented ...
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Abstract: In this paper, we propose a multistep extension of the Shanks sequence transformation. It is defined as a ratio of determinants. Then, we show that this transformation can be recursively implemented by a multistep extension of the $\varepsilon$–algorithm of Wynn. Some of their properties are specified. Thereafter, the multistep $\varepsilon$–algorithm and the multistep Shanks transformation are proved to be related to an extended discrete Lotka–Volterra system. These results are obtained by using Hirota’s bilinear method, a procedure quite useful in the solution of nonlinear partial differential and difference equations.
This paper presents an iterative scheme for the solution of the large matrix equations arising in the full-wave electromagnetic analysis of printed antenna arrays. The proposed technique is based on the Jacobi decompo...
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