在海洋数据同化领域,集合最优插值方法中,矩阵求逆过程所使用的奇异值分解(singular value decomposition,SVD)十分耗时。对集合最优插值中逆矩阵的求逆过程进行优化,分别使用LU分解、Choleskey分解、QR分解来替代SVD分解。首先,通过LU...在海洋数据同化领域,集合最优插值方法中,矩阵求逆过程所使用的奇异值分解(singular value decomposition,SVD)十分耗时。对集合最优插值中逆矩阵的求逆过程进行优化,分别使用LU分解、Choleskey分解、QR分解来替代SVD分解。首先,通过LU分解(Choleskey分解或QR分解)得到相应的三角矩阵(或正交矩阵);然后,利用分解后的矩阵来实现相关逆矩阵的计算。由于LU分解、Choleskey分解、QR分解的算法复杂度都远小于SVD分解,因此改进后的同化程序能得到大幅度的性能提升。数值结果表明,所采用的三种矩阵分解方法相比于SVD分解,都能将集合最优插值的计算效率提升至少两倍以上。值得一提的是,在四种矩阵分解中Choleskey分解使得整个同化程序的性能达到了最优。展开更多
This paper proposes a novel algorithm, which can be used to model and analyzemesh tree hybrid power/ground distribution networks with multiple voltage supply in time domain.Not only this algorithm enhances common meth...This paper proposes a novel algorithm, which can be used to model and analyzemesh tree hybrid power/ground distribution networks with multiple voltage supply in time domain.Not only this algorithm enhances common method''s ability on analysis of power/ground network withirregular topology, but also very high accuracy it keeps. The accuracy and stability of thisalgorithm is proved using strict math method in this paper. Also, the usage of both preconditiontechnique based on Incomplete Choleskey Decomposition and fast variable elimination technique hasimproved the algorithm''s efficiency a lot. Experimental results show that it can finish the analysisof power/ground network with enormous, size within very short time. Also, this algorithm can beapplied to analyze the clock network, bus network, and signal network without buffer under highworking frequency because of the independence of the topology.展开更多
文摘在海洋数据同化领域,集合最优插值方法中,矩阵求逆过程所使用的奇异值分解(singular value decomposition,SVD)十分耗时。对集合最优插值中逆矩阵的求逆过程进行优化,分别使用LU分解、Choleskey分解、QR分解来替代SVD分解。首先,通过LU分解(Choleskey分解或QR分解)得到相应的三角矩阵(或正交矩阵);然后,利用分解后的矩阵来实现相关逆矩阵的计算。由于LU分解、Choleskey分解、QR分解的算法复杂度都远小于SVD分解,因此改进后的同化程序能得到大幅度的性能提升。数值结果表明,所采用的三种矩阵分解方法相比于SVD分解,都能将集合最优插值的计算效率提升至少两倍以上。值得一提的是,在四种矩阵分解中Choleskey分解使得整个同化程序的性能达到了最优。
文摘This paper proposes a novel algorithm, which can be used to model and analyzemesh tree hybrid power/ground distribution networks with multiple voltage supply in time domain.Not only this algorithm enhances common method''s ability on analysis of power/ground network withirregular topology, but also very high accuracy it keeps. The accuracy and stability of thisalgorithm is proved using strict math method in this paper. Also, the usage of both preconditiontechnique based on Incomplete Choleskey Decomposition and fast variable elimination technique hasimproved the algorithm''s efficiency a lot. Experimental results show that it can finish the analysisof power/ground network with enormous, size within very short time. Also, this algorithm can beapplied to analyze the clock network, bus network, and signal network without buffer under highworking frequency because of the independence of the topology.
