This paper presents a novel reduced-order algorithm for identifying rational models. From the Arnoldi process, an orthonormal basis of the Krylov subspace is constructed. Based on the Krylov subspace, a high-order cos...
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This paper presents a novel reduced-order algorithm for identifying rational models. From the Arnoldi process, an orthonormal basis of the Krylov subspace is constructed. Based on the Krylov subspace, a high-order cost function is transformed into a low-order one, thereby significantly reducing the computational efforts. This algorithm can be considered as a reduced-order least squares (LS) algorithm or an extension of the traditional gradient iterative (GI) algorithm for different Krylov subspaces, and it presents several advantages over the traditional LS and GI algorithms. The simulated numerical results/figures are consistent with the analytically derived results in terms of the feasibility and effectiveness of the proposed algorithm. (C) 2021 Elsevier Ltd. All rights reserved.
reduced-order identification algorithms are usually used in machine learning and big data technologies, where the large-scale systems widely exist. For large-scale system identification, traditional least squares algo...
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reduced-order identification algorithms are usually used in machine learning and big data technologies, where the large-scale systems widely exist. For large-scale system identification, traditional least squares algorithm involves high-order matrix inverse calculation, while traditional gradient descent algorithm has slow convergence rates. The reduced-order algorithm proposed in this paper has some advantages over the previous work: (1) via sequential partitioning of the parameter vector, the calculation of the inverse of a high-order matrix can be reduced to low-order matrix inverse calculations;(2) has a better conditioned information matrix than that of the gradient descent algorithm, thus has faster convergence rates;(3) its convergence rates can be increased by using the Aitken acceleration method, therefore the reduced-order based Aitken algorithm is at least quadratic convergent and has no limitation on the step-size. The properties of the reduced-order algorithm are also given. Simulation results demonstrate the effectiveness of the proposed algorithm. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
This study presents the introduction of the reduced-order, 1.5-D versions of the TESLA-family of 2.5-D large-signal codes, which have been implemented by simplifications in the particle's motion model by its restr...
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This study presents the introduction of the reduced-order, 1.5-D versions of the TESLA-family of 2.5-D large-signal codes, which have been implemented by simplifications in the particle's motion model by its restriction in a single, z-direction only. This in effect assumes that the guiding magnetic field is infinite what leads to a complete elimination of any transverse motion of particles, including their radial motion and rotation. Such simplifications in the algorithms allow reach up to two-times improvement in their performance due to significantly reduced number of operations, but they also in effect reduce an overall dimensionality of the algorithms from 2.5-D to 1.5-D only. The results of the modeling performed by the newly introduced 1.5-D versions of TESLA-family of large-signal codes and their comparisons with the results of modeling by the original 2.5-D algorithms are discussed in detail. Results of this study allow find accuracy and range of applicability of the 1.5-D large-signal codes and help to determine the place of such reduced-order algorithms.
In this paper, the numerical algorithm for solving the state and output feedback H-infinity-constrained LQG control problem is investigated. Although the equations that have to be solved to design the controller consi...
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In this paper, the numerical algorithm for solving the state and output feedback H-infinity-constrained LQG control problem is investigated. Although the equations that have to be solved to design the controller consist of the nonlinear cross-coupled algebraic Riccati equations ( CAREs), it is newly proven that both the uniqueness and the positive semidefiniteness of the iterative solutions can be guaranteed when disturbance attenuation level gamma is sufficiently large. The computational examples are given to demonstrate the efficiency of the proposed algorithm. (C) 2007 Elsevier Inc. All rights reserved.
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