大规模非对称线性方程组Lanczos算法和精化Lanczos算法的对比  

The Comparison of Lanczos Method and Refined Lanczos Method for Large Unsymmetric Linear Systems

作　　者：张亚蕾 杨少静 ZHANG Ya-lei;YANG Shao-jing(Mathematics Department,Yang-en University,Quanzhou 362014,Fujian,China;Department of Public Lesson,Hebei College of Science and Technology,Baoding 071000,Hebei,China)

机构地区：[1]仰恩大学数学系,福建泉州362014 [2]河北科技学院公共课部,河北保定071000

出　　处：《山西师范大学学报（自然科学版）》2020年第3期17-22,共6页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：2017年福建省教育厅中青年教育科研项目(科技类)(项目编号:JAT170723).

摘　　要：为了得到更加符合大规模非对称线性方程组的求解算法提出了Lanczos算法和精化Lanczos算法的对比分析,利用构建三角矩阵精化向量子空间的Ritz值和投影方式进行精细化对比,发现精化Lanczos算法的精细度高出102,接着分析算法的计算速度得出收敛效果的对比结果,在此基础上对比两种算法的时间消耗和内存消耗,得出精化Lanczos算法可以节省约30 s时间消耗和二分之一内存空间消耗的结论,最后通过计算残量值和特征值对比算法计算结果,经过对比分析充分凸显精化Lanczos算法的多方面优势.In order to obtain a solution algorithm that conforms to the large unsymmetric linear equations,a comparative analysis of Lanczos algorithm and refined Lanczos algorithm is proposed,and a fine comparison is made by constructing the Ritz value and projection method of triangular matrix refinement to quantum space.I found the precision of the refined Lanczos algorithm is higher,and then analyzed the calculation speed of the algorithm to obtain a comparative result of the convergence effect.On this basis,the time consumption and memory consumption of the two algorithms were compared.It is concluded that the refined Lanczos algorithm can save about 30 s time consumption and one-half memory space consumption.Finally,the results of calculating the residual value and eigenvalue comparison algorithm are calculated.After comparative analysis,the multiple advantages of the refined Lanczos algorithm are fully highlighted.

关 键 词：非对称性方程组 LANCZOS算法 精化Lanczos算法 

分 类 号：O241[理学—计算数学]