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10th International Symposium on Distributed Computing and Applications to Business, Engineering and Science (DCABES)

作者： Yan, Yongxin Zhang, Xiaolei Wu, Xuesong Cao, Jianwen Chinese Acad Sci Inst Software Lab Parallel Software & Computat Sci Beijing Peoples R China Beijing Univ Posts & Telecommun Int Sch Beijing 100088 Peoples R China

ISBN: (纸本)9780769544151

The mathematical modeling and simulation based on the Modelica language usually gets a high-index differential-algebraic equation (DAE) system. The structural index reduction algorithms can serve as a fast method to reduce such high-indexed issues. In order to solve the failure of the structural index reduction algorithms in some cases, the combinatorial (1)relaxation algorithm is analyzed and studied. Finally, the result of an example shows the combinatorial relaxation algorithm is an effective way to improve the stability of the index reduction algorithms based on the structural index of DAE.

关键词： Modelica differential-algebraic equation index reduction combinatorial relaxation algorithm

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Detecting and correcting the index of DAE by the combinatorial relaxation algorithm

Detecting and correcting the index of DAE by the combinatori...

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2011 IEEE 10th International Symposium on Distributed Computing and Applications to Business,Engineering(第十届电子商务、工程及科学领域的分布式计算和应用国际学术研讨会 DCABES 2011)

作者： Xiaolei Zhang Yongxin Yan Xuesong Wu Jianwen Cao International School Beijing University of Posts and Telecommunications Beijing China Laboratory of Parallel Software and ComputationalScience the Institute of SoftwareChinese Academy o Laboratory of Parallel Software and Computational Science the Institute of Software Chinese Academ

The mathematical modeling and simulation based on the Modelica language usually gets a high-index differential-algebraic equation (DAE) system. The structural index reduction algorithms can serve as a fast method to reduce such high-indexed issues. In order to solve the failure of the structural index reduction algorithms in some cases, the combinatorial 1relaxation algorithm is analyzed and studied. Finally, the result of an example shows the combinatorial relaxation algorithm is an effective way to improve the stability of the index reduction algorithms based on the structural index of DAE.

关键词： Modelica differential-algebraic equation index reduction combinatorial relaxation algorithm

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Detecting and correcting the index of DAE by the combinatorial relaxation algorithm

Detecting and correcting the index of DAE by the combinatori...

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第十届电子商务、工程及科学领域的分布式计算和应用（DCABES）国际学术研讨会

作者： Yongxin Yan,Xiaolei Zhang International School Beijing University of Posts and Telecommunications Beijing,China Xuesong Wu*,Jianwen Cao Laboratory of Parallel Software and Computational Science,the Institute of Software,Chinese Academy of Sciences Beijing,China

The mathematical modeling and simulation based on the Modelica language usually gets a high-index differential-algebraic equation(DAE) *** structural index reduction algorithms can serve as a fast method to reduce such high-indexed *** order to solve the failure of the structural index reduction algorithms in some cases,the combinatorial 1 relaxation algorithm is analyzed and ***,the result of an example shows the combinatorial relaxation algorithm is an effective way to improve the stability of the index reduction algorithms based on the structural index of DAE.

关键词： Modelica differential-algebraic equation index reduction combinatorial relaxation algorithm

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Computing the Degree of Determinants via Discrete Convex Optimization on Euclidean Builuiags

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SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY 2019年第3期3卷 523-557页

作者： Hirai, Hiroshi Univ Tokyo Grad Sch Informat Sci & Technol Dept Math Informat Tokyo 1138656 Japan

In this paper, we consider the computation of the degree of the Dieudonne determinant of a linear symbolic matrix A = A(0) + A(1)x(1) + ...+ A(m)x(m), where each A is an n x n polynomial matrix over K[t] and x(1), x(2), ..., x m are pairwise "noncommutative" variables. This quantity is regarded as a weighted generalization of the noncommutative rank (nc-rank) of a linear symbolic matrix, and its computation is shown to be a generalization of several basic combinatorial optimization problems, such as weighted bipartite matching and weighted linear matroid intersection problems. Based on the work on nc-rank by Fortin and Reutenauer [Sem. Lothar. Combin., 52 (2004), B52f] and Ivanyos, Qiao, and Subrahmanyam [Comput. Complex., 27 (2018), pp. 561-593], we develop a framework to compute the degree of the Dieudonne determinant of a linear symbolic matrix. We show that the deg-det computation reduces to a discrete convex optimization problem on the Euclidean building for SL(K(t)(n)). To deal with this optimization problem, we introduce a class of discrete convex functions on the building. This class is a natural generalization of L-convex functions in discrete convex analysis (DCA). We develop a DCA-oriented algorithm (steepest descent algorithm) to compute the degree of determinants. Our algorithm works with matrix computation on K and uses a subroutine to compute a certificate vector subspace for the nc-rank, where the number of calls of the subroutine is sharply estimated. Our algorithm enhances some classical combinatorial optimization algorithms with new insights, and it is also understood as a variant of the combinatorial relaxation algorithm, which was developed earlier by Murota for computing the degree of the (ordinary) determinant.

关键词： noncommutative rank Dieudonne determinant skew field discrete convex analysis mixed matrix combinatorial relaxation algorithm submodular function L-convex function Euclidean building uniform modular lattice

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