Splitting methods for tensor equations |
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| Authors: | Dong‐Hui Li Shuilian Xie Hong‐Ru Xu |
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| Affiliation: | 1. School of Mathematical Sciences, South China Normal University, Guangzhou, China;2. School of Mathematics, Jiaying University, Meizhou, China |
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| Abstract: | The Jacobi, Gauss‐Seidel and successive over‐relaxation methods are well‐known basic iterative methods for solving system of linear equations. In this paper, we extend those basic methods to solve the tensor equation  , where  is an m th‐order n ?dimensional symmetric tensor and b is an n ‐dimensional vector. Under appropriate conditions, we show that the proposed methods are globally convergent and locally r‐linearly convergent. Taking into account the special structure of the Newton method for the problem, we propose a Newton‐Gauss‐Seidel method, which is expected to converge faster than the above methods. The proposed methods can be extended to solve a general symmetric tensor equations. Our preliminary numerical results show the effectiveness of the proposed methods. |
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| Keywords: | convergence polynomial optimization splitting methods tensor equation |
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