论文摘要
本文主要研究了完全非正rational Bernstein-Vandermonde矩阵、逆完全非正rational Bernstein-Vandermonde矩阵和rational Said-Ball-Vandermonde矩阵的奇异值、特征值以及线性系统解的高精度算法.文中分别构造出了这三类矩阵.在第二章中,计算了rational Bernstein-Vandermonde完全非正类矩阵的奇异值和线性系统的精确解.在第三章中,讨论了两类rational基的逆完全非正类配置矩阵的高精度计算问题.对于这三类矩阵都是通过Neville消元法,将其双对角分解后,再重新参数化,并结合我们已有的算法进行高精度计算.最后,通过数值实验验证该算法的精确性.
论文目录
文章来源
类型: 硕士论文
作者: 马潇潇
导师: 黄荣
关键词: 高精度,完全非正矩阵,逆完全非正矩阵,消元法,参数化
来源: 湘潭大学
年度: 2019
分类: 基础科学
专业: 数学
单位: 湘潭大学
分类号: O151.21
DOI: 10.27426/d.cnki.gxtdu.2019.000530
总页数: 48
文件大小: 1488K
下载量: 9
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