Characterization of Extreme Points of Multi-Stochastic Tensors
| العنوان: | Characterization of Extreme Points of Multi-Stochastic Tensors |
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| المؤلفون: | Mingqing Xiao, Rihuan Ke, Wen Li |
| المصدر: | Computational Methods in Applied Mathematics. 16:459-474 |
| بيانات النشر: | Walter de Gruyter GmbH, 2016. |
| سنة النشر: | 2016 |
| مصطلحات موضوعية: | Computational Mathematics, Numerical Analysis, Pure mathematics, Applied Mathematics, 010102 general mathematics, Convex combination, 010103 numerical & computational mathematics, 0101 mathematics, Extreme point, Characterization (mathematics), 01 natural sciences, Mathematics |
| الوصف: | 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 paper, we focus on studying stochastic tensors and, in particular, we study the extreme points of a set of multi-stochastic 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 multi-stochastic tensors ( n = 3 ${n=3}$ 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. |
| تدمد: | 1609-9389 1609-4840 |
| DOI: | 10.1515/cmam-2016-0005 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::197710472c2b3e333111adb2e12452cd https://doi.org/10.1515/cmam-2016-0005 |
| رقم الانضمام: | edsair.doi...........197710472c2b3e333111adb2e12452cd |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 16099389 16094840 |
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| DOI: | 10.1515/cmam-2016-0005 |