【摘 要】
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Stochastic matrices play an important role in the study of probability theory and statistics, and are often used in a variety of modeling problems in econom
【机 构】
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SouthChinaNormalUniversity
【出 处】
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2016年张量和矩阵学术研讨会(International conference on Tensor, Matrix a
论文部分内容阅读
Stochastic matrices play an important role in the study of probability theory and statistics, and are often used in a variety of modeling problems in economics, biology and operation research. Recently, the study of tensors and their applications became a hot topic in numerical analysis and optimization. In this talk, we focus on studying stochas-tic tensors and, in particular, we study the extreme points of a set of multistochastic tensors. Two necessary and sufficient conditions for a multi-stochastic tensor to be an extreme point are established. These conditions characterize the generators of multi-stochastic tensors. An algorithm to search the convex combination of extreme points for an arbitrary given multi-stochastic tensor is developed. Based on our obtained results, some expression properties for third-order and n-dimensional multistochastic tensors (n=3 and 4) are derived, and all extreme points of 3-dimensional and 4-dimensional triply-stochastic tensors can be produced in a simple way. As an application, a new approach for the partially filled square problem under the framework of multi-stochastic tensors is given.
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