一类预条件AOR迭代法的比较定理.pdf

数 学 杂 志 Vo1．34(2014) No．3 J．ofMath．(PRC) C0M PARISoN THE0REM S FoR A CLASS oF PRECoNDIT10NED A0R ITERATIVE M ETH0DS XUEQiu—fang，一．GAOXing—bao．LIUXiao—guang (』．CollegeofMath．andInfor．Science，ShaanxiNormalUniversity，Xian710062，China) (2．DepartmentofAppliedMath．，Xi’anUniversityofTechnology，Xi’an7~oo48，China) Abstract： Inthispaper，thepreconditionedA0R iterativemethodswiththepreconditioners 一 arestudiedwhenthecoefficientmatrixofthelinearsystem isastrictlydiagonallydominant L—matrix．Byusing therelated theoriesofmatrix splitting，theconvergenceperformanceofthe DreconditionedA0R methodsandthecomparisontheoremsabouttheinfluenceoftheparameters OLand ontherateofconvergenceareobtained．TheresultsindicatethattheDreconditionerswith thebig and areefficientandcompetitivefortheDreconditk’nedAOR methods．Theresults in thepapergeneralizethoseaboutthepreconditionedGauss—SeidelmethodsgivenbyLieta1． Numerica1examplesfurtherverifvtheresults． Keywords： preconditi0ner；preconditionedA0R iterativemethod；strictlydiagonallydom— inantL —matrix；spectralradius 2010 M R Subiect Classification： 65F10 DocumentCOde： A ArticleID： 0255-7797f2014103—0448—13 1 Introduction Considerthelargesparselinearsystem z= b． whereX，b∈R andA：(aij)∈R isnonsingular．Itiswellknownthatthissystemoften arisesfrom computationalfluiddynamics，thermal，structuralandcircuitsimulatorproblems andusuallyissolvedbytheiterativemethods．LetA ：M —N andM benonsingular，then thebasiciterativemethod iS k+1= Txk+C， ： 0，1，… ， whereT = M 一 N istheiterativematrix．C= M ～b． W ithoutlossofgenerality，in thispaper，weletA = I—L 一 whereIisart×n identitymatrix．-Land— arethestrictlylower