| Status | 已發表Published |
| Some recent developments in matrix analysis and computation | |
Jin, X. Q.; Vong, S. W. ; Xie, Z. J.; Zhao, Z.
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| 2019-05-30 | |
| Source Publication | Proceedings of the Seventh International Congress of Chinese Mathematicians, Volume II
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| Abstract | This article is divided into three parts. In the first part, we study preconditioners for tensors. New definitions for Toeplitz tensors and circulant tensors are given. Moreover, an optimal preconditioner for tensors is proposed from a theoretical viewpoint. Böttcher and Wenzel proposed the following conjecture in 2005: the least upper bound of the Frobenius norm of the commutator of any real matrices X; Y ∈ Rn×n is given by ∥XY −YX∥F ≤ √2 ∥X∥F∥Y∥F. We give an elementary proof of the conjecture in the second part. In the last part, we study the stochastic inverse eigenvalue problem. We first reformulate this problem as a Riemannian optimization problem, and then we propose a geometric nonlinear conjugate gradient algorithm for solving the problem. Numerical results show the efficiency of our method for solving large-scale problems. |
| Keyword | Preconditioner Toeplitz tensor commutator norm inequality stochastic inverse eigenvalue problem Riemannian optimization |
| Language | 英語English |
| The Source to Article | PB_Publication |
| PUB ID | 55080 |
| Document Type | Conference paper |
| Collection | DEPARTMENT OF MATHEMATICS |
| Recommended Citation GB/T 7714 | Jin, X. Q.,Vong, S. W.,Xie, Z. J.,et al. Some recent developments in matrix analysis and computation[C], 2019. |
| APA | Jin, X. Q.., Vong, S. W.., Xie, Z. J.., & Zhao, Z. (2019). Some recent developments in matrix analysis and computation. Proceedings of the Seventh International Congress of Chinese Mathematicians, Volume II. |
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