In order to fast extract the frequency-dependent parameters of on-chip interconnects with lossy substrate, the fast discrete Hadamard transform (FDHT) is adopted to sparsify the dense matrix formed by the complex diel...
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In order to fast extract the frequency-dependent parameters of on-chip interconnects with lossy substrate, the fast discrete Hadamard transform (FDHT) is adopted to sparsify the dense matrix formed by the complex dielectric image method which is accelerated by the epsilon-algorithm of the Pade approximation and GMRES iteration is used to solve the resulted sparse matrix equations.
The minimum singular functional control problem is analyzed for a class of multi-input affine nonlinear systems under the hypothesis that the associated Lie algebra is nilpotent. The optimal control corresponding to t...
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The minimum singular functional control problem is analyzed for a class of multi-input affine nonlinear systems under the hypothesis that the associated Lie algebra is nilpotent. The optimal control corresponding to the first, second, and third order nilpotent operators is determined. We develop an algorithm for solving the singular problem that is applicable whether or not singular subarcs exist in the optimal control.
The epsilon-algorithm is well known as a numerical tool for accelerating the convergence of sequences. It is shown empirically that this property holds for convergent series in the general sense of distributions. This...
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The epsilon-algorithm is well known as a numerical tool for accelerating the convergence of sequences. It is shown empirically that this property holds for convergent series in the general sense of distributions. This means that, at singular points, the epsilon-algorithm also accelerates the divergence, and clearly reveals the presence of delta functions as well as other singularities such as 1/x, step functions.... As an example, the solution of an integral equation in a problem of electrostatics, developed as a series of Legendre polynomials, has been analyzed by the epsilon-algorithm. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.
A new type of generalized matrix inverse is used to define the generalized inverse matrix Pade approximants (GMPA), GMPA is introduced on the basis of scalar product of matrices, with the form of matrix numerator and ...
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A new type of generalized matrix inverse is used to define the generalized inverse matrix Pade approximants (GMPA), GMPA is introduced on the basis of scalar product of matrices, with the form of matrix numerator and scalar denominator. It is different from the existing matrix Pade approximants in that it does not need multiplication of matrices in the construction process. Some algebraic properties are discussed. The representations of GMPA are provided with the following three forms: (i) the explicit determinantal formulas for the denominator scalar polynomials and the numerator matrix polynomials;(ii) E-algorithm expression;(iii) Thiele-type continued fraction expression. The equivalence relations above three representations are proposed. (C) 2001 Elsevier Science Inc. All rights reserved.
作者：
Senhadji, MNUSTL
Lab Analyse Numer & Optimisat F-59655 Villeneuve Dascq France Univ Oran
Inst Math Es Senia Algeria
Quasi-linear functions generate sequence transformation methods whose conditioning depends upon the nature of the sequence to be accelerated. These methods are often well conditioned when they are applied to alternati...
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Quasi-linear functions generate sequence transformation methods whose conditioning depends upon the nature of the sequence to be accelerated. These methods are often well conditioned when they are applied to alternating sequences;however, they are relatively ill-conditioned in case of monotonic convergence. The condition numbers of the Shanks transformation e(k)((n)) are given in order to prove that the closely related epsilon -algorithm to a such transformation is ill-conditioned when performed on the set of totally monotonic sequences. In the same way, we show that this algorithm is well conditioned on the set of totally oscillating sequences. (C) 2001 Elsevier Science B.V. All rights reserved.
The present paper is a survey of the most popular vector extrapolation methods such as the reduced rank extrapolation (RRE), the minimal polynomial extrapolation (MPE), the modified minimal polynomial extrapolation (M...
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The present paper is a survey of the most popular vector extrapolation methods such as the reduced rank extrapolation (RRE), the minimal polynomial extrapolation (MPE), the modified minimal polynomial extrapolation (MMPE), the vector epsilon-algorithm (VEA) and the topological epsilon-algorithm (TEA), Using projectors, we derive a different interpretation of these methods and give some theoretical results. The second aim of this work is to give a numerical comparison of the vector extrapolation methods above When they are used for practical large problems such as linear and nonlinear systems of equations. (C) 2000 Elsevier Science B.V. All rights reserved.
The vector epsilon-algorithm is a generalization of Aitken Delta(2)-process to the vector cast. It has been used for solving a system of linear and nonlinear equations. The acceleration properties of the hybrid proced...
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The vector epsilon-algorithm is a generalization of Aitken Delta(2)-process to the vector cast. It has been used for solving a system of linear and nonlinear equations. The acceleration properties of the hybrid procedures have been also studied for solving a system of linear equations. In this paper, we consider the vector epsilon-algorithm and hybrid procedures for solving some unconstrained nonlinear optimization problems. A convergence acceleration result is established and numerical examples are given, (C) 1999 Elsevier Science B.V. and IMACS. All rights reserved.
One of the well-known convergence acceleration methods, the epsilon-algorithm is investigated from the viewpoint of the Toda molecule equation. It is shown that the error caused by the algorithm is evaluated by means ...
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One of the well-known convergence acceleration methods, the epsilon-algorithm is investigated from the viewpoint of the Toda molecule equation. It is shown that the error caused by the algorithm is evaluated by means of solutions for the equation. The acceleration algorithm based on the discrete Toda molecule equation is also presented.
The epsilon-algorithm is a quite powerful algorithm for accelerating the convergence of some classes of sequences. It was generalized in two different ways some years ago. In this paper, a determinantal formula for it...
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The epsilon-algorithm is a quite powerful algorithm for accelerating the convergence of some classes of sequences. It was generalized in two different ways some years ago. In this paper, a determinantal formula for its second generalization is obtained. Then its kernel (the set of sequences which are transformed into a constant sequence) is given as the solution of a difference equation.
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