An approach to solve the problem of synthesizing stable algorithms for adaptation of dynamic objects with a control delay is proposed. It was demonstrated that the problem of calculating a pseudo-inverse matrix for ob...
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ISBN:
(纸本)9783030352493;9783030352486
An approach to solve the problem of synthesizing stable algorithms for adaptation of dynamic objects with a control delay is proposed. It was demonstrated that the problem of calculating a pseudo-inverse matrix for object control is generally unstable with respect to matrix perturbations. To solve equation for control law, A.N. Tikhonov's methods of regularization and singular decomposition are used based on the minimal pseudo-inverse matrix. The proposed computational schemes enable the synthesis of object adaptation stable algorithms with control delay and provide high quality control processes.
We present fast and numerically stable algorithms for the solution of linear systems of equations, where the coefficient matrix can be written in the form of a banded plus semiseparable matrix. Such matrices include b...
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We present fast and numerically stable algorithms for the solution of linear systems of equations, where the coefficient matrix can be written in the form of a banded plus semiseparable matrix. Such matrices include banded matrices, banded bordered matrices, semiseparable matrices, and block-diagonal plus semiseparable matrices as special cases. Our algorithms are based on novel matrix factorizations developed specifically for matrices with such structures. We also present interesting numerical results with these algorithms.
For the recently introduced algorithms to solve the time-dependent Maxwell equations [J. S. Kole, M. T. Figge, and H. De Raedt, Phys. Rev. E 64, 066705 (2001)], we construct a variable grid implementation and an impro...
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For the recently introduced algorithms to solve the time-dependent Maxwell equations [J. S. Kole, M. T. Figge, and H. De Raedt, Phys. Rev. E 64, 066705 (2001)], we construct a variable grid implementation and an improved spatial discretization implementation that preserve the exceptional property of the algorithms to be unconditionally stable by construction. We find that the performance and accuracy of the corresponding algorithms are significant and illustrate their practical relevance by simulating various physical model systems.
Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for on...
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Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for one-, two-, and three-dimensional systems with spatially varying permittivity and permeability. The salient features of the algorithms are illustrated by computing selected eigenmodes and the full density of states of one-, two-, and three-dimensional models and by simulating the propagation of light in slabs of photonic band-gap materials.
An equilibrium system (also known as a Karush-Kuhn-Tucker (KKT) system, a saddlepoint system, or a sparse tableau) is a square linear system with a certain structure. Strang [SIAM Rev., 30 (1988), pp. 283-297] has obs...
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An equilibrium system (also known as a Karush-Kuhn-Tucker (KKT) system, a saddlepoint system, or a sparse tableau) is a square linear system with a certain structure. Strang [SIAM Rev., 30 (1988), pp. 283-297] has observed that equilibrium systems arise in optimization, finite elements, structural analysis, and electrical networks. Recently, Stewart [Linear Algebra Appl., 112 (1989), pp. 189-193] established a norm bound for a type of equilibrium system in the case when the ''stiffness'' portion of the system is very ill-conditioned. This paper investigates the algorithmic implications of Stewart's result. It is shown that several algorithms for equilibrium systems appearing in applications textbooks are unstable. A certain hybrid method is then proposed, and it is proved that the new method has the right stability property.
In applied sciences, the analysis of Bessel and Airy oscillatory integrals is a demanding problem, particularly for large-scale data points and large frequency parameters. The Levin method, with global radial basis fu...
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In applied sciences, the analysis of Bessel and Airy oscillatory integrals is a demanding problem, particularly for large-scale data points and large frequency parameters. The Levin method, with global radial basis functions, is an accurate tool for approximating these integrals. But as the interpolation points or frequency increase, the interpolation matrix becomes dense and highly ill-conditioned. To ensure a stable and efficient computation of Bessel and Airy integrals, we implement the Levin method with compactly supported radial basis functions. Although the accuracy of the new algorithm has not significantly improved compared to the counterpart methods. Alternatively, the method exhibits faster and well-conditioned behavior, even for large numbers of data points and large frequency parameters. The convergence analysis of the method is performed and numerically verified with several benchmark problems.
A new fast and stable algorithm to reduce a symmetric banded plus semi-separable matrix to tridiagonal form via orthogonal similarity transformations is presented. (C) 2000 Elsevier Science Inc. All rights reserved.
A new fast and stable algorithm to reduce a symmetric banded plus semi-separable matrix to tridiagonal form via orthogonal similarity transformations is presented. (C) 2000 Elsevier Science Inc. All rights reserved.
We address the discrete inverse conductance problem for well-connected spider networks, that is, to recover the conductance function on a well-connected spider network from the Dirichlet-to-Neumann map. It is well-kno...
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We address the discrete inverse conductance problem for well-connected spider networks, that is, to recover the conductance function on a well-connected spider network from the Dirichlet-to-Neumann map. It is well-known that this inverse problem is exponentially ill-posed, requiring the implementation of a regularization strategy for numerical solutions. Our focus lies in exploring whether prior knowledge of the conductance being piecewise constant within a partition of the edge set comprising a few subsets enables stable conductance recovery. To achieve this, we propose formulating the problem as a polynomial optimization problem, incorporating a regularization term that accounts for the piecewise constant hypothesis. We show several experimental examples in which the stable conductance recovery under the aforementioned hypothesis is feasible.
A new, efficient, and stable algorithm for computing all the eigenvalues and eigenvectors of the problem Ax = lambda Bx, where A is symmetric indefinite and B is symmetric positive definite, is proposed.
A new, efficient, and stable algorithm for computing all the eigenvalues and eigenvectors of the problem Ax = lambda Bx, where A is symmetric indefinite and B is symmetric positive definite, is proposed.
A two-way chasing algorithm to reduce a diagonal plus a symmetric semi-separable matrix to a symmetric tridiagonal one and an algorithm to reduce a diagonal plus an unsymmetric semi-separable matrix to a bidiagonal on...
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A two-way chasing algorithm to reduce a diagonal plus a symmetric semi-separable matrix to a symmetric tridiagonal one and an algorithm to reduce a diagonal plus an unsymmetric semi-separable matrix to a bidiagonal one are considered. Both algorithms are fast and stable, requiring a computational cost of N-2, where N is the order of the considered matrix.
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