由Lanczos方法具体构造BiCG算法相关的理论研究

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	由Lanczos方法具体构造BiCG算法相关的理论研究
Alternative Title	Studies 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 Abstract	In 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
Identifier	https://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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