A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors
We consider multilinear systems of equations whose coefficient tensors are (Formula presented.)-tensors. Multilinear systems of equations have many applications in engineering and scientific computing, such as data mining and numerical partial differential equations. In this paper, we show that solv...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/67006 |
| _version_ | 1848761450242244608 |
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| author | He, H. Ling, C. Qi, L. Zhou, Guanglu |
| author_facet | He, H. Ling, C. Qi, L. Zhou, Guanglu |
| author_sort | He, H. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We consider multilinear systems of equations whose coefficient tensors are (Formula presented.)-tensors. Multilinear systems of equations have many applications in engineering and scientific computing, such as data mining and numerical partial differential equations. In this paper, we show that solving multilinear systems with (Formula presented.)-tensors is equivalent to solving nonlinear systems of equations where the involving functions are P-functions. Based on this result, we propose a Newton-type method to solve multilinear systems with (Formula presented.)-tensors. For a multilinear system with a nonsingular (Formula presented.)-tensor and a positive right side vector, we prove that the sequence generated by the proposed method converges to the unique solution of the multilinear system and the convergence rate is quadratic. Numerical results are reported to show that the proposed method is promising. |
| first_indexed | 2025-11-14T10:31:52Z |
| format | Journal Article |
| id | curtin-20.500.11937-67006 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:31:52Z |
| publishDate | 2018 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-670062019-03-15T05:48:10Z A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors He, H. Ling, C. Qi, L. Zhou, Guanglu We consider multilinear systems of equations whose coefficient tensors are (Formula presented.)-tensors. Multilinear systems of equations have many applications in engineering and scientific computing, such as data mining and numerical partial differential equations. In this paper, we show that solving multilinear systems with (Formula presented.)-tensors is equivalent to solving nonlinear systems of equations where the involving functions are P-functions. Based on this result, we propose a Newton-type method to solve multilinear systems with (Formula presented.)-tensors. For a multilinear system with a nonsingular (Formula presented.)-tensor and a positive right side vector, we prove that the sequence generated by the proposed method converges to the unique solution of the multilinear system and the convergence rate is quadratic. Numerical results are reported to show that the proposed method is promising. 2018 Journal Article http://hdl.handle.net/20.500.11937/67006 10.1007/s10915-018-0689-7 fulltext |
| spellingShingle | He, H. Ling, C. Qi, L. Zhou, Guanglu A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors |
| title | A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors |
| title_full | A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors |
| title_fullStr | A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors |
| title_full_unstemmed | A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors |
| title_short | A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors |
| title_sort | globally and quadratically convergent algorithm for solving multilinear systems with m-tensors |
| url | http://hdl.handle.net/20.500.11937/67006 |