【摘要】：數(shù)據(jù)的敏感性是許多領(lǐng)域都會涉及的問題、關(guān)注的對象,自進入大數(shù)據(jù)時代,數(shù)值計算中的敏感性分析更是研究中的重點,如何有效利用海量的數(shù)據(jù),提取出有用信息,創(chuàng)造更大的價值,在天文、建筑、經(jīng)濟等領(lǐng)域都有著重要的應(yīng)用。在《數(shù)值分析》中我們學習了線性方程組右端和系數(shù)矩陣整體誤差對于解的影響,為了更加有效的利用海量數(shù)據(jù),本篇論文主要利用線性方程組問題來討論單一數(shù)據(jù)的誤差對解的影響,希望篩選出對解的精度有較大影響的數(shù)據(jù),對其精度進行有效控制,而影響較小的數(shù)據(jù),可以放寬其精度的要求,從而達到工作效率的提高。本文也對已有的完全最小二乘法的研究進行了介紹以及我在最小二乘法的敏感性分析的研究過程及結(jié)果的介紹。本篇論文的結(jié)構(gòu)如下.第一章簡單介紹了數(shù)據(jù)敏感性分析的研究背景以及本文的主要結(jié)果,第二章主要介紹研究線性方程組單一數(shù)據(jù)誤差的敏感性分析及相關(guān)結(jié)果,第三章是對最小二乘法的敏感性進行深入分析及討論,第四章總結(jié)了這段時間的工作內(nèi)容及得出的結(jié)果并討論了未來的工作方向。
[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.
【學位授予單位】：吉林大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O241

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本文編號：2216964