廣義自反矩陣和廣義反自反矩陣的最小二乘及其最佳逼近問題.pdf

1、湖南大學(xué)碩士學(xué)位論文廣義自反矩陣和廣義反自反矩陣的最小二乘及其最佳逼近問題姓名：劉學(xué)杰申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：胡錫炎20070519碩士學(xué)位論文AbstractTheconstrainedmatrixequationproblemhasbeenwidelyusedincontroltheycivilengineering，vibrationthey，economyfieldengineeringcalculations

2、oon.Thispaperstudiesthefollowingquestionsoftheleastsquarestheoptimalapproximationsolutionofthegeneralizedreflexivematricesgeneralizedantireflexivematrices:Problem1:GivenmatrixXBfindAinSsuchthatAX=BwhereSisthegivensetofma

3、trix.Problem2:GivenmatrixXBfindAinSsuchthat?AX?B?=minwhereSisthegivensetofmatrix.Problem3:GivenmatrixMfindNinSEsuchthat?M?N?=inf?M?A?whereSEisthesolutionsetofProblem1Problem2?.?istheFrobeniusnm.Themainresultsofthispapera

4、reasfollows:1.WhenSisthesetofgeneralizedreflexivematricesgeneralizedantireflexivematriceswehaveobtainedthesolvabilityofthesufficientnecessaryconditionsofProblem1theexpressionsofsolutionsofProblems2，3byusingtheacterconstr

5、uctionoftwokindsofmatrices.Atthesametimewehavealsogiventhenumericalexampletosupptourtheeticalresults.2.WhenSisthesetofreflexivematricesantireflexivematricesonthelinearmanifold，byapplyingtheacterconstructionoftwokindsofma

6、trices，wehavediscussedtheProblems23obtainedtheexpressionsofsolutionsofProblem2theoptimalapproximationofProblem3.AtthesametimetheproblemsofmatrixequationAXXA=Chavingnonemptysolutionsetinthegeneralizedreflexivematricestheg

7、eneralizedantireflexivematricesareconsideredtheirgeneralexpressionareprovided.3.WhenSisthesetofgeneralizedreflexivematricesgeneralizedantireflexivematricesonthelinearmanifold，wehaveobtainedtheexpressionsofsolutionsofProb

8、lem2theoptimalapproximationofProblem3.ThethesisissupptedbytheNationNaturalScienceFoundationofChina.KeyWds:ConstrainedmatrixequationGeneralizedreflexivematricesGeneralizedantireflexivematricesLeastsquaressolutionOptimalap