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A divide and conquer algorithm for constrained multibody system dynamics based on augmented Lagrangian method with projections-based error correction

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NONLINEAR DYNAMICS 2012年第1期70卷 871-889页

作者： Malczyk, Pawel Fraczek, Janusz Warsaw Univ Technol Fac Power & Aeronaut Engn Inst Aeronaut & Appl Mech PL-00665 Warsaw Poland

This paper presents a new parallel algorithm for dynamics simulation of general multibody systems. The developed formulations are iterative and possess divide and conquer structure. The constraints equations are imposed at the acceleration level. Augmented Lagrangian methods with mass-orthogonal projections are used to prevent from constraint violation errors. The proposed approaches treat tree topology mechanisms or multibody systems which contain kinematic closed loops in a uniform manner and can handle problems with rank deficient Jacobian matrices. Test case results indicate good accuracy performance dependent on the expense put in the iterative correction of constraint equations. Good numerical properties and robustness of the algorithms are observed when handling systems with single and coupled kinematic loops, redundant constraints, which may repeatedly enter singular configurations.

关键词： divide and conquer algorithm Augmented Lagrangian method Mass-orthogonal projections Parallel computing

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A divide and conquer algorithm FOR THE SUPERFAST SOLUTION OF TOEPLITZ-LIKE SYSTEMS

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2012年第4期33卷 1039-1056页

作者： Favati, Paola Lotti, Grazia Menchi, Ornella CNR IIT I-56124 Pisa Italy Univ Parma Dept Math I-43100 Parma Italy Univ Pisa Dipartment Comp Sci I-56127 Pisa Italy

In this paper a new O(N log(3) N) solver for N x N Toeplitz-like systems, based on a divide and conquer technique, is presented. Similarly to the superfast algorithm MBA for the inversion of a Toeplitz-like matrix [R. R. Bitmead and B. D. O. Anderson, Linear Algebra Appl., 34 (1980), pp. 103-116;M. Morf, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 1980, pp. 954-959], it exploits the displacement properties. In order to avoid the well-known numerical instability of the explicit inversion, the new algorithm relies on the triangular factorization and back-substitution formula for the system seen as a 2x2 block system with blocks of half size. This idea is the one used in [M. Stewart, SIAM J. Matrix Anal. Appl., 25 (2003), pp. 669-693] to improve the numerical stability of superfast methods based on the generalized Schur algorithm for positive definite Toeplitz matrices, but the algorithm we propose can be applied also to nonsymmetric Toeplitz-like systems. The stability of the algorithm is examined through numerical experiments.

关键词： divide and conquer algorithm superfast algorithm Toeplitz-like matrices

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A divide and conquer algorithm on the double dimensional inverse eigenvalue problem for Jacobi matrices

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APPLIED MATHEMATICS AND COMPUTATION 2012年第8期219卷 3840-3846页

作者： Wu, Xiaoqian Donghua Univ Dept Appl Math Coll Sci Shanghai 201620 Peoples R China

This paper proposes a divide and conquer algorithm for reconstructing a 2nth order Jacobi matrix J(2n) with a given nth order leading principal submatrix J(n) and with all eigenvalues of J(2n). This algorithm needs to compute the eigenvalues of the nth order Jacobi matrix J'(n+1),(2n) and the first components of the unit eigenvectors of J'(n+1),(2n), where J'(n+1),(2n) = J(n+1),(2n) - beta(n)e(1)e(1)(T). The method needs not to reconstruct the leading principal submatrix J(n), and can avoid computing the coefficients of the characteristic polynomial for getting the eigenvalues of J(n). (C) 2012 Elsevier Inc. All rights reserved.

关键词： divide and conquer algorithm Symmetric tridiagonal matrix Jacobi matrix Eigenvalue problem Inverse eigenvalue problem Double dimension problem

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A Robust divide and conquer algorithm for Progressive Medial Axes of Planar Shapes

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2016年第12期22卷 2522-2536页

作者： Liu, Yong-Jin Yu, Cheng-Chi Yu, Min-Jing Tang, Kai Kim, Deok-Soo Tsinghua Univ Dept Comp Sci & Technol TNList Beijing Peoples R China Hong Kong Univ Sci & Technol Dept Mech & Aerosp Engn Hong Kong Hong Kong Peoples R China Hanyang Univ Voronoi Diagram Res Ctr Seoul South Korea Hanyang Univ Sch Mech Engn Seoul South Korea

The medial axis is an important shape representation that finds a wide range of applications in shape analysis. For large-scale shapes of high resolution, a progressive medial axis representation that starts with the lowest resolution and gradually adds more details is desired. In this paper, we propose a fast and robust geometric algorithm that computes progressive medial axes of a large-scale planar shape. The key ingredient of our method is a novel structural analysis of merging medial axes of two planar shapes along a shared boundary. Our method is robust by separating the analysis of topological structure from numerical computation. Our method is also fast and we show that the time complexity of merging two medial axes is O(n log n(v)), where n is the number of total boundary generators, n(v) is strictly smaller than n and behaves as a small constant in all our experiments. Experiments on large-scale polygonal data and comparison with state-of-the-art methods show the efficiency and effectiveness of the proposed method.

关键词： Progressive medial axes shape hierarchy and evolution topology-oriented algorithm divide and conquer algorithm

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TOWARDS A divide-AND-conquer algorithm FOR THE REAL NONSYMMETRIC EIGENVALUE PROBLEM

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 1994年第4期15卷 1333-1353页

作者： ADAMS, L ARBENZ, P SWISS FED INST TECHNOL INST WISSENSCHAFTL RECHNEN ZENTRUM CH-8092 ZURICH SWITZERLAND

Theory is developed that could be used towards developing a divide and conquer algorithm for the nonsymmetric eigenvalue problem. The shortcomings of this theory and its application to the Hessenberg and nonsymmetric tridiagonal problems are discussed. The conclusion is made that the method may not be as promising as the divide and conquer methods for symmetric problems.

关键词： TRIDIAGONAL MATRIX HEISSENBERG MATRIX MODIFIED EIGENVALUE PROBLEM divide and conquer algorithm

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A Selection Problem for Management Based on divide and conquer algorithm

A Selection Problem for Management Based on Divide and Conqu...

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IITA International Conference on Control, Automation and Systems Engineering

作者： Wang, Xiaohui Zhang, Yong Zhao, Hongyan Shandong Univ Finance Sch Comp & Informat Engn Jinan Peoples R China Shandong Agr Univ Econ Management Coll Tai An Shandong Peoples R China Shandong Yingcai Univ Sch Comp & Informat Engn Jinan Peoples R China

ISBN: (纸本)9780769537283

Selection problem, which is to find the k th smallest element in a sequence of n numbers in arbitrary order, is a typical problem in algorithm design and analysis. The select problem is solved by divide and conquer algorithm. The general algorithm is given, and the complexity of this algorithm is analyzed and discussed. The divide and conquer algorithms are related to backfitting and Markov chain Monte Carlo techniques, which divide the problem in a divide and conquer strategy into smaller pieces. Confidence intervals taking model uncertainty into account are based on the bootstrap in combination with MCMC techniques.

关键词： selection problem MCMC divide and conquer algorithm

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Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm

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NONLINEAR DYNAMICS 2020年第3期102卷 1611-1626页

作者： Dabiri, Arman Poursina, Mohammad Machado, J. A. Tenreiro Southern Illinois Univ Edwardsville Dept Mech & Mechatron Engn Edwardsville IL 62026 USA Univ Agder Dept Sci & Engn N-4879 Grimstad Norway Polytech Inst Porto Inst Engn Dept Elect Engn Rua Dr Antonio Bernardino de Almeida 431 P-4249015 Porto Portugal

In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws.

关键词： Multibody dynamics Closed-chain system Open-chain system LQR Optimal control divide and conquer algorithm Computed-torque control Fractional control PID Parallel computing

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An improved divide-and-conquer algorithm for the banded matrices with narrow bandwidths

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2016年第10期71卷 1933-1943页

作者： Liao, Xiangke Li, Shengguo Cheng, Lizhi Gu, Ming Natl Univ Def Technol Coll Comp Changsha 410073 Hunan Peoples R China Natl Univ Def Technol Sci & Technol Parallel & Distributed Proc Lab Changsha 410073 Hunan Peoples R China Natl Univ Def Technol State Key Lab High Performance Comp Changsha 410073 Hunan Peoples R China Natl Univ Def Technol Coll Sci Changsha 410073 Hunan Peoples R China Univ Calif Berkeley Dept Math Berkeley CA 94720 USA

In this paper we propose a novel divide-and-conquer (DC) algorithm to compute the SVD of banded matrices, and further accelerate it by using rank-structured matrix techniques, especially the hierarchically semiseparable (HSS) matrix. The DC algorithm for the symmetric banded eigenvalue problem can also be accelerated similarly. For matrices with few deflations, the banded DC algorithms require more flops than the classical DC algorithm, and thus they are suitable for narrowly banded matrices. While, if there exist many deflations, the banded DC algorithms can be faster than the classical ones for matrices with relatively large bandwidths. Numerous experiments have been done to test the proposed algorithms. Some of the tested matrices are from construction and some are from real applications. Comparing with the DC algorithm in Intel MKL, our proposed algorithms can be hundreds times faster for matrices with narrow bandwidths or many deflations. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： divide and conquer algorithm Banded matrices SVD HSS matrices Eigenvalue problem

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A Selection Problem for Management Based on divide and conquer algorithm

A Selection Problem for Management Based on Divide and Conqu...

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IITA International Conference on Control, Automation and Systems Engineering

作者： Xiaohui Wang Yong Zhang Hongyan Zhao School of Computer & Information Engineering Shandong University of Finance Economy & Management College Shandong Agricultural University School of Computer & Information Engineering Shandong Yingcai University

ISBN: (纸本)9781424445530

关键词： Selection problem MCMC divide and conquer algorithm

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divide-AND-conquer algorithmS FOR THE BANDSYMMETRIC EIGENVALUE PROBLEM

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PARALLEL COMPUTING 1992年第10期18卷 1105-1128页

作者： ARBENZ, P ETH Zentrum Institut für Wissenschaftliches Rechnen 8092 Zürich Switzerland

divide and conquer algorithms are formulated for the solution of the eigenvalue Problem for symmetric band matrices. The new algorithms are compared to the traditional solution paths offered by EISPACK, tridiagonaliza... 详细信息

关键词： EIGENVALUE PROBLEM SYMMETRICAL BAND MATRIX divide and conquer algorithm

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