3矩阵特征值与特征向量的计算

在高压缸排汽的总管上装有动力控制止回阀，以便在事故情况下切断，防止蒸汽返回到汽轮机，引起汽轮机超速。在高压缸排汽总管的端头有蒸汽冲洗接口，以供在管道安装完毕后进行冲洗，在管道冲洗完成后用堵头堵死。centerpinchecksandanchoringtheinnercylinder.AccordingtoWhilecouplingalignmentshouldkeepoiloutofcavityandlocatetherotoraxisneckraisedarewithintheprescribedlimits,thereshouldbenogaps,Horn,HornandHorn0.05mmfeelergaugesfitinto.Centercoupling,condenserwaterfillingandwater-filledaccordingtofactoryrequirement.ForcouplingthreesupportedrotorCenter,themouthunderthecouplingbetweenthevalueshouldbeasstipulatedinthemanufacturer,usually0.15~0.25mm.Inthecaseofcouplingconnection,ifpossible,liftingonlyonebearingendofthesupportbearingoftherotor,removethebearing,fittedwithspecialtilesandspecialliftingtools,discrotors,checkthejournalfluttertile,shouldgenerallybelessthan0.10MM.Whenthecouplingsandrotorcomeswhenthereisaconflict,thecouplingCentreshallprevail.6.4.5.2.2shaftlookingfor:...6.4.5.3.Provisionalboltconfirmedthepositioningoftherotorsize,aswellasthecouplingbetweentheadjustmentshimthicknessaccuracy,drawingstomeetthetechnicalrequirements.Plane,cylindricalandcleanthecouplingboltholesshouldbecleanandwithoutburrs,scrapironandgrease-free,relativepositionofthecouplingaccordingtothedrawingrequirementsare.Couplingtopscrews,rounddistanceapart,indicatorstomonitormovementoftheaircraft,itsvalueisallowedtopassthevalueaxismoving,mountedadjustmentpads,notepadsinstallationdirectionguidepincouplingwithprocessendclosed.Thebackwheelsslowlytightened,when2mmorso,withstandardwhitebarswheretwobackwheelboltholemeasurementaboveandbelow,confirmtwobackwheelboltholeconcentricity.Then,thesymmetricalhorizontalmounttwotemporaryboltstightened,attentiontomonitordialindicator,theninstallthesymmetricaltemporarybolts,thistimesitesslowlymovingrotor,inthemeasuredcircumferenceof8equalpartsbackwheelrimrock,eachmeasuringrelativechangesinvalueshouldbelessthan0.02mm.6.4.5.4couplingreamedandpairedboltreamingdiereamer,adjustablereamers,boringmill,inseveralways.6.4.5.4.1Generalrequirementsbeforereamingorboring,第3章矩阵特征值与特征向量的计算一些工程技术问题需要用数值方法求得矩阵的全部或部分特征值及相关的特征向量。3.1特征值的估计较粗估计(A)||A||欲将复平面上的特征值一个个用圆盘围起来。3.1.1盖氏图定义3.1-1设A=[aij]nn，称由不等式nijjijiiaaz1所确定的复区域为A的第i个盖氏图，记为Gi，i=1，2，…，n。}:{1nijjijiiiaazzG定理3.1-1若为A的特征值，则niiG1证明：设Ax=x(x0)，若k使得xxxinik1max因为knjjkjxxa1nkjjkjkkkxaxa)(nkjjkjnkjjkjkjnkjkjkjkkaxxaxxaa11niikGG1例1估计方阵41.03.02.05.013.012.01.035.03.02.01.01A特征值的范围解：在高压缸排汽的总管上装有动力控制止回阀，以便在事故情况下切断，防止蒸汽返回到汽轮机，引起汽轮机超速。在高压缸排汽总管的端头有蒸汽冲洗接口，以供在管道安装完毕后进行冲洗，在管道冲洗完成后用堵头堵死。centerpinchecksandanchoringtheinnercylinder.AccordingtoWhilecouplingalignmentshouldkeepoiloutofcavityandlocatetherotoraxisneckraisedarewithintheprescribedlimits,thereshouldbenogaps,Horn,HornandHorn0.05mmfeelergaugesfitinto.Centercoupling,condenserwaterfillingandwater-filledaccordingtofactoryrequirement.ForcouplingthreesupportedrotorCenter,themouthunderthecouplingbetweenthevalueshouldbeasstipulatedinthemanufacturer,usually0.15~0.25mm.Inthecaseofcouplingconnection,ifpossible,liftingonlyonebearingendofthesupportbearingoftherotor,removethebearing,fittedwithspecialtilesandspecialliftingtools,discrotors,checkthejournalfluttertile,shouldgenerallybelessthan0.10MM.Whenthecouplingsandrotorcomeswhenthereisaconflict,thecouplingCentreshallprevail.6.4.5.2.2shaftlookingfor:...6.4.5.3.Provisionalboltconfirmedthepositioningoftherotorsize,aswellasthecouplingbetweentheadjustmentshimthicknessaccuracy,drawingstomeetthetechnicalrequirements.Plane,cylindricalandcleanthecouplingboltholesshouldbecleanandwithoutburrs,scrapironandgrease-free,relativepositionofthecouplingaccordingtothedrawingrequirementsare.Couplingtopscrews,rounddistanceapart,indicatorstomonitormovementoftheaircraft,itsvalueisallowedtopassthevalueaxismoving,mountedadjustmentpads,notepadsinstallationdirectionguidepincouplingwithprocessendclosed.Thebackwheelsslowlytightened,when2mmorso,withstandardwhitebarswheretwobackwheelboltholemeasurementaboveandbelow,confirmtwobackwheelboltholeconcentricity.Then,thesymmetricalhorizontalmounttwotemporaryboltstightened,attentiontomonitordialindicator,theninstallthesymmetricaltemporarybolts,thistimesitesslowlymovingrotor,inthemeasuredcircumferenceof8equalpartsbackwheelrimrock,eachmeasuringrelativechangesinvalueshouldbelessthan0.02mm.6.4.5.4couplingreamedandpairedboltreamingdiereamer,adjustablereamers,boringmill,inseveralways.6.4.5.4.1Generalrequirementsbeforereamingorboring,G1={z：|z–1|0.6}；G2={z：|z–3|0.8}；G3={z：|z+1|1.8}；G4={z：|z+4|0.6}。注：定理称A的n个特征值全落在n个盖氏圆上，但未说明每个圆盘内都有一个特征值。3.1.2盖氏圆的连通部分称相交盖氏圆之并构成的连通部分为连通部分。孤立的盖氏圆本身也为一个连通部分。定理3.1-2若由A的k个盖氏圆组成的连通部分，含且仅含A的k个特征值。证明:令D=diag(a11，a12，…，ann)，M=A–D，记)10(000)(212211122211nnnnnnaaaaaaaaaMDA则显然有A(1)=A，A(0)=D，易知A()的特征多项式的系数是的多项式，从而A()的特征值1()，2()，…，n()为的连续函数。A()的盖氏圆为：)10(,}||||:{)(11inijjijnijjijiiiGaaazzG因为A(0)=D的n个特征值a11，a12，…，ann，恰为A的盖氏圆圆心，当由0增大到1时，i()画出一条以i(0)=aii为始点，i(1)=i为终点的连续曲线，且始终不会越过Gi；不失一般性，设A开头的k个圆盘是连通的，其并集为S，它与后n–k个圆盘严格分离，显然，A()的前k个盖氏圆盘与后n–k