低秩Hankel张量填充的快速算法  

A fast algorithm for low-rank Hankel tensor completion

作　　者：王川龙[1] 郭雄伟 Chuanlong Wang;Xiongwei Guo

机构地区：[1]太原师范学院工程科学计算山西省高等学校重点实验室,晋中030619

出　　处：《中国科学：数学》2022年第6期729-740,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11371275)资助项目。

摘　　要：基于迭代张量在Hankel张量集上的投影,本文提出一种快速且具有较高精度的Hankel张量填充算法.该算法迭代生成的填充张量保持了Hankel结构,从而减少了奇异值分解的计算量,节约了CPU时间.本文在不增加条件的基础上得到了算法的收敛性,而且修正后的迭代张量更好地逼近了最优解.最后通过数值实验证明新算法比低秩张量填充算法、张量恢复的Douglas-Rachford分解算法、高精度低秩张量填充算法和正交秩1张量填充算法更有效.In this paper,a fast and high accurate algorithm is proposed for the Hankel tensor completion based on the iterative tensor projection onto the Hankel tensor set.The iterative completion tensors generated by the new algorithm keep the Hankel structure,which decreases the computation of SVD(singular value decomposition)and has a better approximation to the solution.The convergence of the new algorithm is obtained by adding conditions and the convergence properties are discussed.Finally,the numerical experiments show that the new algorithm is more effective than the low-rank tensor completion(LRTC)algorithm,Douglas-Rachford splitting for the tensor recovery(DR-TR)algorithm,the high accurate low-rank tensor completion(HaLRTC)algorithm and the orthogonal rank-one tensor pursuit(OR1TP)algorithm.

关 键 词：Hankel张量 张量填充 Hankel化 增广Lagrange乘子法 

分 类 号：O183.2[理学—数学]