### 摘要

We consider the numerical solution of a c-stable linear equation in the tensor product space ℝn1x...xnd, arising from a discretized elliptic partial differential equation in ℝ^{d}. Utilizing the stability, we produce an equivalent d-stable generalized Stein-like equation, which can be solved iteratively. For large-scale problems defined by sparse and structured matrices, the methods can be modified for further efficiency, producing algorithms of O(Σini)+O(ns) computational complexity, under appropriate assumptions (with n_{s} being the flop count for solving a linear system associated with Ai-γIni). Illustrative numerical examples will be presented.

原文 | 英語 |
---|---|

文章編號 | e2106 |

期刊 | Numerical Linear Algebra with Applications |

卷 | 24 |

發行號 | 6 |

DOIs | |

出版狀態 | 已發佈 - 2017 十二月 1 |

### ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics

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## 引用此

Fan, H-Y., Zhang, L., Chu, E. K. W., & Wei, Y. (2017). Numerical solution to a linear equation with tensor product structure.

*Numerical Linear Algebra with Applications*,*24*(6), [e2106]. https://doi.org/10.1002/nla.2106