幾類約束矩陣方程的迭代解法.pdf

1、長沙理工大學碩士學位論文幾類約束矩陣方程的迭代解法姓名：李妍申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：周富照20070401ABSTRACTThec0璐劬Iincdmatfixequati∞pfoblemshavebe蛆widelyappliedinbiOlogy，ele硎cit弘molecul盯spc叫脅scopy，solidmechani娼，s衄lcIumIdesign，6llitcelemenls，par鋤e仃eidentific

2、ation，Vibmtionthcory，automatic∞n缸oIm∞r(nóng)y，line盯optimalcontrol柚d∞∞SolVingtheco璐仃ainedmatri】【cquationproblemsis∞eoftheimponantstIldy咖stentsjnnmnericalline盯algebmneprobl鋤swhichwillbemainlydi鯽s∞dinthcMSthesis眥鶴fonowing：PmbkmIG

3、iv％爿，口∈R辨塒，丘ndX∈S，suchnmtAXBProbkmⅡGiven彳∈R辨Ⅻ，曰∈尺州9，C∈R刪，，矗ndZ∈S，suchthat腳一CPmbkmⅢGiven4∈只吶塒，且∈R刪n，c1∈R^m，彳2∈胄用2研，口2∈月4。^，C2∈R腑2轆，findX∈S，suchtllatM碼tcl，I彳2避c2PmbIemⅣwhenProblemIorIIorⅢc叫sistent，lct&denotethesctofi協(xié)∞luti

4、0璐，givenxo∈R～，findx∈&，叫chthatII碧一工。I|I卿IIx一石。4^口Fwherc00denoteⅡ圮Frobeniusno皿，sisR4塒orasubsctofR4黼satis毋ingsomeconsna缸cOnditio鵬Themainachivementsare勰fbllows：1Wh∞Sarcsy咖etricrcflexivem棚ces，sy刪咀etric鋤thncxivem刪∞s甜sy咖etrizab

5、lematrices，tbe鯽砸cient壯dneccssaryconditio璐underthe∞lVablc柚dthegcneralprovidcdfomofme∞lutionofP加M鋤I一Ⅳhaveb咖obtainedbyme娜ofm刪?；韉咖positi∞sinmanyfcfe坨ncesmthisthesis，the∞lvabilityofthepIoblems伽bedetemlincdautomaticallyduringt

6、heite船tii∞byitc翰tivemethodsPr∞fthatwhenProblemI一Ⅲissolvablc，its∞l塒衄canbeobtainedwithin血itciterativestcps，whensctthcspccialinitialm塒x，thenitsle嬲tn㈣∞lution啪bcobtainedwithin丘nitestcpsFu州k冊0∞，theleast—no徹solutionoftheoptimal