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本文在矩阵P-转置运算的基础上拓广求解T-对称正定大型稀疏矩阵线性代数方程组的平方根法和改进平方根法,并讨论其节省存贮空间的方法。 相似文献
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本文将矩阵P-转置运算拓广为g-转置运算,给出规范g-对称矩阵的三角分解条件及三角分解式,即LL^g及LDL^g分解。 相似文献
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本文提出新一代申威众核架构上稀疏通用矩阵-矩阵乘法(SpGEMM)的并行算法swSpGEMM。设计轻量级并行任务划分有效地应对了矩阵非零元分布引起的负载不均衡问题;针对累加过程中的不规则访存和指令流水低效问题,设计了分层稀疏累加器,在不同输入特征下高效利用申威从核层次化内存,且减少了整数查找中的指令间依赖,更有效地发挥硬件的计算能力。SuiteSparse稀疏矩阵测试集中较大规模输入矩阵上,swSpGEMM的性能相比Intel Skylake双CPU上的MKL和NVIDIA A100上的cuSPARSE分别加速了21.1%和95.3%。 相似文献
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The method of reconstruction of complete deterministic Mueller matrices for the structures of incomplete matrices, which are measured in the method of three input polarizations, has been developed. The method is based on reconstruction of the corresponding Jones matrices for the given structures of incomplete Mueller matrices. 相似文献
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量子力学中的密度矩阵与具有相同密度矩阵的系综的可区分性 总被引:1,自引:0,他引:1
讨论了密度矩阵的不同定义。建议使用完全密度矩阵、压缩密度矩阵和约化密度矩阵分别描写一个封闭量子体系的、一个系综中平均分子的和一个复合体系中的一个子系统的密度矩阵。强调这与现在人们认为的具有相同压缩密度矩阵的系综是完全等价的结论完全不同,具有相同压缩密度矩阵但是成分不同的系综可以通过系综整体测量来区别。作为一个应用,现在认为现有的核磁共振量子计算中没有纠缠的结论是没有根据的。Density matrix is one important tool in quantum mechanics, and it has very broad applications. However there are different definitions about the density matrix, and they describe quite different systems. There has been some misunderstanding about the density matrix in the community, and these misunderstandings hinder the right application of the density matrix. In this article, we discuss the different definitions of density matrix. We suggest to use the full density matrix, compressed density matrix and the reduced density matrix to describe the state of a complete quantum system, the state of an averaged particle in an ensemble and the state of part of a composite system. We stress that contrary to the wide accepted understanding that ensembles with the same compressed density matrix are physically indistinguishable, they are distinguishable through the so-called ensemble measurement. As an application, we suggest that the present conclusion that the present-day nuclear magnetic resonance quantum computation does not have quantum entanglement is groundless. 相似文献
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Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix 总被引:1,自引:0,他引:1
Gui Lu Long Yi-Fan Zhou Jia-Qi Jin Yang Sun Hai-Woong Lee 《Foundations of Physics》2006,36(8):1217-1243
We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed. 相似文献
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多自由度线性微幅振动系统简正坐标的一般求法 总被引:4,自引:0,他引:4
给出了动能矩阵为对角矩阵,在A=aE和A≠aE(E为单位矩阵)两种情况下同时对角化势能矩阵求简正坐标的一般方法,并提出了先改变坐标标度,后对角化新势能矩阵或用频率特征矩阵的伴随矩阵的任一列求简正坐标的另两种方法. 相似文献
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Pasha Zusmanovich 《Journal of Nonlinear Mathematical Physics》2013,20(3):431-439
We present an elementary heuristic reasoning based on Arnold's theory of versal deformations in support of a straightforward algorithm for finding a correlation matrix near a given symmetric one. 相似文献
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本文用T矩阵与场方程叠加相结合的方法,系统研究任意方位双球粒子体系散射矩阵各元素随两球球心的间距变化规律。 详细推导了双球粒子体系T矩阵的具体形式,并将T矩阵所求得的散射矩阵与单个球的情况作了比较。数值计算表明,球心间间距的增加对该体系的散射矩阵影响不大,得出任意方位即对方位求平均的情况下,双球粒子体系的散射矩阵与体系中有较大尺寸参数的单球相似的结论. 相似文献
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