幾類矩陣擴(kuò)充問(wèn)題和兩類約束矩陣方程問(wèn)題.pdf

1、長(zhǎng)沙理工大學(xué)碩士學(xué)位論文幾類矩陣擴(kuò)充問(wèn)題和兩類約束矩陣方程問(wèn)題姓名：熊培銀申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：周富照20070401ABSTRACTTheprobl鋤ofmatrixe，【￡哪ionis，under∞meconstrainedconditioIl，to∞nstmctm砒rices4withagiV鋤matrixAo勰its蛐bm砌x；Theprobl咖oftlleconmfainedmatrix唧l撕onist0f

2、indtllesoluti∞ofm枷x(chóng)equationinsomem枷cesset，ttlefollowingproblemsareconsideredPI砸blemIIGiV蚰Ⅳ，占∈R刪研，幾∈4sRp9(R弘9)，l≤口≤療，6nd彳∈爿艘蘆”(“cjsR肼”)，飄lchthtAx=口，4=4(【1：q】)Pl劬blemⅡGiVenX，曰∈月；彳o∈sR9。9(爿sR9加，R9。4)，1≤g≤玎，find4∈墨，suchtht以=

3、4(【l：g】)whereSisthe∞Iutionsetof，(一)=J眇一圳=嘲，彳∈艘(4膿4”，D2膿)PmblemⅢGiv∞二i∈尺～，findj∈S，叭chthat阻五忙咧p40whereSisthe∞hnionsetofProblemIorⅡPmbIemⅣGiVenz∈R舭‘，y∈R刪1，c∈R舭‘，曰∈R刪‘，find一∈R男(R!笛)，suchthat／(爿)=I眇一口02曠A—c7112=minPmbIemVGive

4、Il4∈Rtind4∈S，跚chthat卜j卜卿卜爿0whe糟whereSisthesohltionsetofProbIemⅣBy印plyingtheSVD、GSVD、QSVD，the∞luable踟伍ciem柚dn∞essaryconditions柚dtheg∞eral∞lutionofProbl哪I，Ⅱa∞g～蛐，tlIeoptimal印pro)【imate∞Iuti∞0fProbIemⅢisfhld咄Byusing舭charane

5、rofthereaIgeneralren麟iveandanti一柵喇vemalricesthegenefalsoluti∞ofprobl鋤IV鋤dappr0嫡mate∞lutionofProblemVamobtained，tlle眥meralalgo血llIIls柚dtheex枷plesofo砸maIappm虹mati∞∞lutiona他giv鈕Keyword摹：Matrjxextension；Constrajnedmatrixequa