数值计算中的敏感性分析
发布时间：2018-09-01 10:50
【摘要】：数据的敏感性是许多领域都会涉及的问题、关注的对象,自进入大数据时代,数值计算中的敏感性分析更是研究中的重点,如何有效利用海量的数据,提取出有用信息,创造更大的价值,在天文、建筑、经济等领域都有着重要的应用。在《数值分析》中我们学习了线性方程组右端和系数矩阵整体误差对于解的影响,为了更加有效的利用海量数据,本篇论文主要利用线性方程组问题来讨论单一数据的误差对解的影响,希望筛选出对解的精度有较大影响的数据,对其精度进行有效控制,而影响较小的数据,可以放宽其精度的要求,从而达到工作效率的提高。本文也对已有的完全最小二乘法的研究进行了介绍以及我在最小二乘法的敏感性分析的研究过程及结果的介绍。本篇论文的结构如下.第一章简单介绍了数据敏感性分析的研究背景以及本文的主要结果,第二章主要介绍研究线性方程组单一数据误差的敏感性分析及相关结果,第三章是对最小二乘法的敏感性进行深入分析及讨论,第四章总结了这段时间的工作内容及得出的结果并讨论了未来的工作方向。
[Abstract]:The sensitivity of data is a problem that will be involved in many fields. Since the period of big data, sensitivity analysis in numerical calculation has been the focus of research. How to effectively use massive data to extract useful information, Create greater value and have important applications in astronomy, architecture, economics and so on. In numerical Analysis, we study the effects of the global error of the right end and coefficient matrix of linear equations on the solution, in order to make more effective use of massive data. In this paper, the problem of linear equations is used to discuss the effect of the error of a single data on the solution. We hope to screen out the data which has a great influence on the accuracy of the solution, and to control the accuracy of the data effectively, but to have less effect on the data. The requirement of precision can be relaxed and the working efficiency can be improved. This paper also introduces the existing research on the complete least square method and the research process and results of my sensitivity analysis in the least squares method. The structure of this paper is as follows. The first chapter briefly introduces the research background of data sensitivity analysis and the main results of this paper. The second chapter mainly introduces the sensitivity analysis of the single data error of linear equations and the related results. In the third chapter, the sensitivity of the least square method is analyzed and discussed in depth. In the fourth chapter, the work contents and the results obtained during this period are summarized and the future work direction is discussed.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241
本文编号：2216964
[Abstract]:The sensitivity of data is a problem that will be involved in many fields. Since the period of big data, sensitivity analysis in numerical calculation has been the focus of research. How to effectively use massive data to extract useful information, Create greater value and have important applications in astronomy, architecture, economics and so on. In numerical Analysis, we study the effects of the global error of the right end and coefficient matrix of linear equations on the solution, in order to make more effective use of massive data. In this paper, the problem of linear equations is used to discuss the effect of the error of a single data on the solution. We hope to screen out the data which has a great influence on the accuracy of the solution, and to control the accuracy of the data effectively, but to have less effect on the data. The requirement of precision can be relaxed and the working efficiency can be improved. This paper also introduces the existing research on the complete least square method and the research process and results of my sensitivity analysis in the least squares method. The structure of this paper is as follows. The first chapter briefly introduces the research background of data sensitivity analysis and the main results of this paper. The second chapter mainly introduces the sensitivity analysis of the single data error of linear equations and the related results. In the third chapter, the sensitivity of the least square method is analyzed and discussed in depth. In the fourth chapter, the work contents and the results obtained during this period are summarized and the future work direction is discussed.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241
【参考文献】
相关期刊论文 前1条
1 刘新国;关于TLS的可解性及扰动分析[J];应用数学学报;1996年02期
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