二次參數方程組線性化處理方法.pdf

1、上海大學碩士學位論文二次參數方程組線性化處理方法姓名：林磊申請學位級別：碩士專業(yè)：計算數學指導教師：顧桂定200604012006年上海大學碩士學位論文IIAbstractInthisthesis，wediscussthenumericalmethodsfors01vingquadraticparameterizedequations(^2A^Bc)￡n)=，Quadraticparameterizedequationsariseina

2、Varietyofpractical印plications，forinstance】chemlmericalmethodsforsolVi“gpartimdi丹bentialequations，controltheory’structuraldynamics，andQcDproblemsSohowtoderiVeae矗bctiverlumericalmethodisimpoTtaDtSpecially，whenthecoe幣dentm亂

3、riceare1盯ge，andthep盯aJneterishuge(afewhundreds)，thee扛bctiVen腳ericalmethodisnecess甜MInthi8thesis，weroundlydiscussquadraticparameterizedequationsweintrodllcethreeprim盯ymethods：1inearization，seriesexpandingandprojectionWbco

4、nsiderturningQPEto曲iftedlinearsystems，tosolvequadraticparameterizedequan伽s工nthispaper，wemainly1lseline棚zationtos01Vequadraticp盯ameterizedequationsDi髓rentLine砸izationcanindueediⅡbrentn、蛐eTicalsolutionspecially，weanabzethe

5、Tdationofsolu_tionandparameterandcoe幣cientmatricesNumeric出experime址sreportchedi髓renteLfectivenessofdi如rentLine時izationThkthesiscanbedjvidedintothrccpartsFirstly，weintroducethespectraltheoryaboutquadraticmatrixandtllreeki

6、ndsofmechodsusedtosolvequadraticp缸ameterizedequ砒ionSecondlyweintroduceKrylovsubspacemethodstosloveshi代edlinearsystemsFinallyweintroducethoselnodestolinearquadraticparameterizedequatbllsNuⅡ培ricalexperiⅡlentsshowallresults