兰州大学机构库 >数学与统计学院
由Lanczos方法具体构造BiCG算法相关的理论研究
Alternative TitleStudies on constructing BiCG Algorithm from Lanczos aspects
张强
Thesis Advisor尤传华
2002-05-12
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword双正交BICG算法 lanczos算法
Abstract本文针对大型矩阵求解 问题,介绍了 子空间的几种迭代算法及相关理论,通过对双正交 算法和 算法的具体比较我们知道这两类方法均归为同一理论,由此我们得到在对双正交Lanczos算法的构造过程和Tm分解时作一特殊处理,便会得到BiCG算法,同时具体给出了这一分解过程及此时所满足的条件。
Other AbstractIn this paper, we have discussed some algorithms based on the Krylow Subspace. These algorithms is useful in solving the problem AX=b. When A is nonsymmtric. Especially, We analyses the Lanczos Biorthogonalization algorithm and the BiCG algorithm and the theorem of them. We know that the both algorithms are theoretically equivalent. The solutions obtained by both algorithms satisfy, Where is such that Therefore,for both methods and the are solutions of linear system. We will complete such things, First the Lanczos Biorthogonalization algorithm is modified accordingly, and then proceeding in the same manner as for the derration of the Conjugate Gradient Algorithm from the symmetric Lanczos algorithm, We write the LDU decomposition of , We will get the BiCG Algorithm . Some theoretical results will be given in this paper.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224385
Collection数学与统计学院
Recommended Citation
GB/T 7714
张强. 由Lanczos方法具体构造BiCG算法相关的理论研究[D]. 兰州. 兰州大学,2002.
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