% Copyright (C) 2018 Liu Yifan, Zhao Tianyu
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% 求解多右端线性方程组的一种改进共轭梯度算法研究\\
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\begin{abstract}
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目前在众多学科领域都需要求解多右端项线性方程组，本文
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到校正矩阵Frobenius范数的最小值。最后通过Julia程序对其进行对比数值试验。
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{\bfseries 关键词: 关键词1,关键词2} }
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At present, it is necessary to solve multi-right-end linear equations in many disciplines. This paper
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algorithms can converge to the minimum of the Frobenius norm value.
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{\bf Keywords:
KW1,KW2} }
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\zihao{3} \bfseries 论文题目
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\section*{结论}
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本文从最优化理论出发
\begin{enumerate}
\item 针对基于Krylov子空间的迭代算法——共轭梯度算法，
\item 在阐述清楚共轭
\item 最后讨论针...进而给出两者的等价性证明。
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\addcontentsline{toc}{section}{参\ 考\ 文\ 献}
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\section*{\centerline{致\hspace*{3em}谢}}
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四年的大学时光流逝的飞快，非常荣幸能够有机会在大学的最后时刻完成这篇致谢，向一直帮助我的师长、家人和朋友们表达我最衷心的感谢。回顾大学四年的学习与生活，我收获了许多，也成长了许多。
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