矩阵分解方法的讨论+文献综述
关键词:矩阵的三角分解,QR 分解,最大秩分解,奇异值分解,非负矩阵分解
毕业设计说明书（论文）外文摘要
Title Discussion of matrix decomposition
Abstract
Economic theory of mathematic , engineering , Management Sciences are
involing the matrix theory of knowledge .Therefore , the matrix theory is
one of the essential foundation for learning and study these subject.
Matrix decomposition on matrix calculation theory and modern mathematics
has played a key role in the development .The so-called matrix
decomposition is written in a matrix structure which is simpler with the
nature of the other matrix multiplication and addition. Matrix
decomposition methods are mainly made of LU triangular decomposition,
Givens QR decomposition method, Household QR decomposition method, matrix
maximum rank decomposition, spectral decomposition of simple matrices.
Non - negative matrix factorization is a kind of all the elements in the
matrix are non - negative constraints of matrix decomposition methods.
The idea for human processing large-scale data provides a new way, with
implementation simplicity, decomposition and decomposition results in the
form of interpretable, and take up less storage space and many other
advantages. NMF can be used for processing, data compression and feature
extraction of dimension reduction
Keywords :LU matrix decomposition ,QR matrix decomposition, maximum rank
decomposition, singular value decomposition, non-negative matrix
decomposition
目次
1 引言2
2 矩阵的三角分解
2.1 消元过程的矩阵描述3
2.2 矩阵的三角分解4
2.3 常用的三角分解公式 „.10
3 矩阵的 QR（正交三角）分解
3.1 QR分解的概念„17
3.2 QR分解的实际求法„19
4 矩阵的最大秩分解27
5 矩阵的奇异值分解30
6 非负矩阵分解
6.1 NMF 背景介绍„.33
6.2 NMF 的实现算法 33
6.3 收敛性证明35
6.4 算法„36
6.5 算法优点与不足37
总结..39
致谢„42
参考文献„41 本科毕业设计说明书（论文） 第2 页 共 46页
1 引言
在近代数学、工程技术、经济理论管理科学中，大量涉及到矩阵理论的知识。
因此，矩阵理论自然就是学习和研究上述学科必不可少的基础之一。另一方面，
矩阵理论发展到今天，已经形成了一整套的理论和方法，内容非常丰富。矩阵分
解对于矩阵理论及近代计算数学的发展起到了关键的作用。寻求矩阵各种意义下