Jacobi矩陣與中心和反中心對稱矩陣逆特征值問題.pdf

1、湖南大學碩士學位論文Jacobi矩陣與中心和反中心對稱矩陣逆特征值問題姓名：馬昌社申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：胡錫炎2002.5.8ABSTRACTThereareallkindsofinverseeigenvalueandgeneralizedinverseeigenvalueproblemsinthefieldsofstructuraldesign，vibrationsystem，automationcontrolan

2、dmatrixdecisionetcAcompoundinverseeigenvalueproblemofJacobimatrixandsomegeneralizedinverseeigenvalueproblemshavebeendiscussedinthispaperFromspecialtonormal，theproblemofconstructingaJacobimatrixwithaprescribedprinciplesub

3、matrixandtwoordereddefectiveeigen—pairshasbeensolvedgraduallyinthispaperFirstwediscussthecasethatthedefectiveeigenvectsarethemaximumandtheminimal；thenthemaximumandthenextmaximum，themaximumandthegeneral；andthecasethatalla

4、regeneralinthelastBasedontherelationshipbetweentheeigenvalueorderandthenumberofvariationsofthecorrespondingeigenvector，somenecessaryandsufficientconditionsforthesolvabilityoftheaboveproblemshavebeenderived，andthecorrespo

5、ndingalgorithmsaredevelopedatthesametimeNumericalexperimentsshowthatthesealgorithmsarequitereliableandefficientBasedonthefoundationalpropertiesofcentrosymmetricmatrixandanti—centrosymmetricmatrix，employingthetechnologyof

6、lowingdimension，thegeneralizedinverseeigenvalueproblemswhichinvolvecentrosymmetricmatrix，anti—centrosymmetricmatrix，andcompoundcentrosymmetdcmatrixandanti—centrosymmetricmatrix，havebeendiscussedOnthebasisofabove，andemplo

7、yingprojectiontheorytheoptimalapproximationofthemunderspectralconstraintshasbeensolvedTheformulasofgeneralsolutionhavebeen舀veil，aswellastheformulasofoptimalapproximationsolutionandnumericalalgorithmsKeyWords：Jacobimatrix