Multiple Generalized Eigenvalue Decomposition Algorithm in Parallel Based on Weighted Matrix
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摘要: 针对串行广义特征值分解算法实时性差的缺点, 提出了基于加权矩阵的多维广义特征值分解算法. 与串行算法不同, 所提算法能够在一次迭代过程中并行地估计出多维广义特征向量. 平稳点分析表明: 当且仅当算法中状态矩阵等于所需的广义特征向量时, 算法达到收敛状态. 通过对比相邻时刻的状态矩阵模值证明了所提算法的自稳定特性. 所提算法参数选取简单, 实际实施较为容易. 数值仿真和实例应用进一步验证了算法的并行性、自稳定性和实用性.Abstract: In order to overcome the disadvantages of sequential algorithms, such as poor real time, a multiple generalized eigenvalue decomposition algorithm is proposed based on weighted matrix method. Unlike sequential algorithms, the proposed algorithm is able to estimate multiple generalized eigenvectors in parallel only through one iteration procedure. The stationary point analysis shows that the algorithm reaches convergence state if and only if the state matrix is equal to the desired generalized eigenvectors. The self-stabilization characteristics of the proposed algorithm is proved by comparing the state matrix module values of adjacent moments. The proposed algorithm parameters are simple to select and easy to implement in practice. Numerical simulation and example application further verify the parallelism, self-stability and practicality of the algorithm.
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图 5 不同对角矩阵下状态矩阵模值曲线
Fig. 5 The norm curves of the state matrix with different diagonal matrices
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