Splitting methods for tensor equations
| Autor: | Hong-Ru Xu, Dong-Hui Li, Shui-Lian Xie |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Tensor contraction
Algebra and Number Theory Applied Mathematics 010103 numerical & computational mathematics 01 natural sciences Tensor field 010101 applied mathematics Exact solutions in general relativity Cartesian tensor Lanczos tensor Applied mathematics Symmetric tensor Tensor 0101 mathematics Tensor density Mathematics |
| Zdroj: | Numerical Linear Algebra with Applications. 24:e2102 |
| ISSN: | 1070-5325 |
| DOI: | 10.1002/nla.2102 |
| Popis: | Summary 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 Axm−1−b=0, where A is an mth-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. |
| Databáze: | OpenAIRE |
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