| 李寒宇,杨虎.双曲矩阵分解修正问题的一些结果[J].数学研究及应用,2013,33(1):35~44 |
| 双曲矩阵分解修正问题的一些结果 |
| Some Results on the Problem of Updating the Hyperbolic Matrix Factorizations |
| 投稿时间：2011-10-08 修订日期：2012-05-22 |
| DOI：10.3770/j.issn:2095-2651.2013.01.004 |
| 中文关键词: 双曲矩阵分解 双曲QR分解 双曲极分解 修正问题 扰动分析. |
| 英文关键词:hyperbolic matrix factorization hyperbolic QR factorization hyperbolic polar factorization updating problem perturbation analysis. |
| 基金项目:国家自然科学基金(Grant Nos.11201507; 11171361), 重庆市自然科学基金(Grant No.2010BB9215). |
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| 中文摘要: |
| 本文探讨了双曲矩阵分解的修正问题.论文首先给出了修正后矩阵存在双曲矩阵分解的充分条件,接着获得了修正双曲因子的微分不等式与一阶扰动表达式. 所得结果推广了由孙继广给出的经典QR分解修正问题的相应结果. |
| 英文摘要: |
| This paper considers the updating problem of the hyperbolic matrix factorizations. The sufficient conditions for the existence of the updated hyperbolic matrix factorizations are first provided. Then, some differential inequalities and first order perturbation expansions for the updated hyperbolic factors are derived. These results generalize the corresponding ones for the updating problem of the classical QR factorization obtained by Jiguang SUN. |
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