若干特殊矩陣的條件數(shù).pdf

1、目錄mn緒論1l.i本文的基本概念和所要研究的問題11.2本文的研究工作與內(nèi)容安排21.3本文所用的數(shù)學(xué)符號(hào)3第二章矩陣的條件數(shù)52.1弓I52.2向量范數(shù)52.3矩陣范數(shù)62.4矩陣的條件數(shù)82.5矩陣的條件數(shù)的應(yīng)用92.6本章小結(jié)11第三章三角矩陣的條件數(shù)123.1弓It123.2三角矩陣的性質(zhì)153.3特殊三角矩陣條件數(shù)173.4本章小結(jié)25第四章兩對(duì)角矩陣條件數(shù)264.1引言264.2兩對(duì)角矩陣條件數(shù)264.3本章小結(jié)31第五章

2、特殊Toeplitz矩陣條件數(shù)325.1弓|胃325.2特殊Toeplitz矩陣條件數(shù)325.3本章小結(jié)39第六章正定矩陣的條件數(shù)406.1弓H406.2正定矩陣的條件數(shù)406.3本章小結(jié)42本文總結(jié)與展望43蘭44##錯(cuò)45儲(chǔ)敲49IAbstractAbstractConditionnumberisaveryimptantconceptinthematrixthey.Inthispaperweintroducethedefinitio

3、nofthematrixnmanditsbasicproperties.Andfurthermewegettheconceptofconditionnumberanditsbasicproperties.SecondlywegivetheestimationsbothofspectralandFrobeniusnmconditionnumberofasimplespecialtriangelmatrix.Thetwodiagonaltr

4、ianglematrixconditionnumberisalsostudied.FinallybythenaturesofthematrixnmwewillstudythespecialToeplitzmatrixconditionnumberandthepositivedefinitematrixconditionnumber.Atthesametimeinthispaperwewillgivesomesimplenumerical

5、examples.Thesenumericalexamplescanbeusedtoverifytherelevantconclusionsreliability.Thispaperismainlycomposedofsevenchapters:Inthefirstchapterweintroducethebackgroundknowledgeaboutthetheysystemincludingitsdevelopmenthisty.

6、Inthesecondchapterweintroducethedefinitionofthematrixnmitsbasicproperties.Wegetseveralgoodpropertiesaboutconditionnumber.InthethirdchapterwegivetheestimationsbothofspectralandFrobeniusnmconditionnumberofasimplematrix.Att

7、hesametimeintheendofthischapterwegivetwosimplenumericalexamples.Inthefourthchapterbythenaturesofthematrixnmwewillstudythetwodiagonaltrianglematrixconditionnumber.InthefifthchapterwewillstudythespecialToeplitzmatrixcondit

8、ionnumber.Atthesametimewewillgivetwosimplenumericalexamplestoverifytherelevantconclusionsreliability..Inthesixthchapterwewillstudythepositivedefinitematrixconditionnumber.Intheseventhchapterwemakeasummaryaboutthispaperan