若干矩陣方程問題的討論.pdf

1、2∞6屑研究生碩士學位論文Y盧95s3了學校代碼：10269學號：YS03121031霉黎唏忿震擎若干矩陣方程問題的討論院系：壟三鱟瞳熬鱟丕專業(yè)方向：鹽差熬鱟研究方向：熬焦垡熬指導教師：睦墨盞叁燕碩士研究生：：婦鹽墜二oo六年五月上海Abstract1’heconstrainedmatr沒equationproblemis，inaconstrainedmatriXset，矗ndingasolutionofthematr汝equation

2、Di跳rentconstrainedconditionanddi往宅rentmatrixtypewillleadtodi丹breIltcon8trainedmatr詼equationproblemThematrixextensionproblemi8，undersomecons紐‘inedconditions，con8打uctingamatr波AWith8百venmatrixAoasits8ubma乞rix0n1979，HHoch8ta

3、d矗r8tdiscussedtheinverseeigeIlvalueproblemofJacobimatrixA盹erthat，thematrixexten8ionproblemi8ingrea七denlandTheconstrainedmatrixequationproblemandthematr波extensionproblemhaⅣebeenwidelyu8edin8tructuraldynamics，biology’elect

4、ric—ity，molecularspectroscopy，contr01theoryvibrationtheory，nonlinearprogram，dynamicanalysisand80on，sothediscu88ionoftheproblemsabovehasactualandappliedbackgroundInthispaper，wecon8iderseveralkindsofconstrainedmatrixequati

5、onpmblemandmatrixe)(tensionproblemThemainachievernent8瓤easfollow：1Theproblemofconstructingarealsymmetricfivediagon以matri)【厶fromitsdefectiveeigenpair(A，恐)，(p，鹼)，(工，，z2)andaprinciplesubmatrix以isdiscussedSomenecessaryandsum

6、cientconditionsofsolvabilityarederivedAspecialrealsymme七ric矗ve_diagonalmatriXiscon8ideredAnumericalalgorithmandanumericalexperimentare西ven2Theleastnorm，positivesemidefiniteandpositivede最niterealsolutionsofbisymmetricmatr

7、b(equations(ATxA，xA—yAD)=(D，o)areconsideredbyapplyingthegeneralizedsingulaTvaluedecompositionTheleastnormsolutionsofsymmetricand8kewantisymmetricmatrixequations(A丁。x4，xA～yAD)=(D，0)arealsoconsidered。3Theleast—squaress01ut