【毕业论文】三对角矩阵的逆的算法及MATLAB实现.docVIP

PAGE 2014届学士学位毕业论文 三对角矩阵的逆的算法及MATLAB实现 学 号：姓 名： 班 级： 12级专升本班 指导教师： 专 业： 数学与应用数学 系 别： 数学系 完成时间： 年 月 摘要 三对角矩阵在现实生活中有很多的应用，因此三对角矩阵的计算近年来被广泛地研究。分块周期三对角矩阵在科学和工程计算方面应用广泛，块三对角矩阵和分块带状矩阵在数学、物理和工程上的很多问题中都有重要的应用。 本文基于三对角矩阵的结构特点，给出了利用解线性方程组的方法、LU分解的方法求三对角矩阵逆矩阵的新算法，这些新算法运算量小，节省内存，在整个计算过程中，只需要进行较少次的乘除运算，新算法比传统算法的计算复杂度和计算时间要低。 其次，通过算例来表示该算法的有效性和可行性。 最后，利用MATLAB编程来实现三对角矩阵逆矩阵的新算法。 关键词：分块周期三对角矩阵；块三对角矩阵；分块带状三对角矩阵；解线性方程组；LU分解法；逆矩阵；MATLAB Triple diagonal matrix inverse algorithm and MATLAB Abstract Triple diagonal matrix in real life there are many applications, so the triple diagonal matrix calculation was widely studied in recent years. Block periodic triple diagonal matrix is applied widely in science and engineering calculation, and the block triple diagonal matrix block banded matrices in mathematics, physics and engineering has important applications in many of the problems, in this paper, based on the structure characteristics of triple diagonal matrices, is given by using the method of solving linear equations, the recursive method, LU decomposition of the new method to calculate the inverse matrix of triple diagonal matrix algorithm, the new algorithm computational complexity is small, save memory, in the whole computing process, only needs less arithmetic, a new algorithm than the traditional algorithm of computing complexity and computing time. Second by an example to show the feasibility and effectiveness of the algorithm Finally, using MATLAB to realize the triple diagonal matrix inverse matrix of the new algorithm Key words: Block periodic triple diagonal matrix; Block-triple diagonal matrix; Block banded triple diagonal matrix; Solution of linear equations; LU decomposition method; inverse matrix; MATLAB. 目录 TOC \o 1-3 \h \z \u HYPERLINK \l _Toc381396591 1.引言 PAGEREF _Toc381396591 \h 5 HYPERLINK \l _Toc381396592 2.基础知识 PAGEREF _Toc381396592 \h 6 HYPERLINK \l _Toc381396593 2.1 定义1 PAGEREF _Toc381396593 \h 6 HYPERL