关于非负对称矩阵的近似逆矩阵.pdfVIP

数 学 杂 志 Vo1．35(2015) NO．2 J．ofMath．(PRC) A N0TE 0N THE APPR0XIM ATED INVERSE 0F A NoN—NEGATIVE SYM M ETRIC M ATRIX GOU Ting-xun，GAO Xin (SchoolMathem。ticsnndStntistic8，CentralChin。Norm。lUniversity,Wuhan430079,Chin口) Abstract：Thispaperstudiestheissueoftheapproximatedinverseofnonnegativesymmetric matrices．ByusingthematrixS= (8i，J)toapproximateitsinverse，anexplicitboundonthe 7 approximationerrorisobtained，and oneconclusionthattheinverseiswellapproximated tothe order1／fn一11uniformlyforlargeniSalsoproved． Keywords： approximationerror；inverse；symmetric；positiveelements 一 2010MR SubjectClassificati0n： 15A09；15A29；15B48 DocumentCOde： A ArticleID： 0255—7797f2015)02—0207_O7 1 Introduction W hen solvingthesolution fora largesystem oflinearequations，agoodapproximate inverseofthecoefficientmatrixiscruciallyimportantinestablishingfastconvergencerates ofriterativealgorithms．Seetheextensivereviews[1，5，7，2o]．Here，weareconcernedwith anxnsymmetricdiagonallydominantmatricesT=(ti，j)withpositiveelements，i．e．， tiJ= tj 0 and t ti ， ， ， ，j，i=1，… ，n (1．1) Itiseasy to show thatT mustbepositivedefinite． Thiskind ofdiagonally dominant nonnegativematriceshasreceivedwideattention[6，8，10]．In[2，7，91，theproblemson inversesofnonnegativematriceshavebeeninvestigated．Markham [13]andMartinezet a1．[14]studiedthesufficientconditionsthattheinversesofnonnegativematricesareM— matrices．WeproposetoapproximatetheinverseofT，T一，bythematrixS= (8i，J)， where 5iJ 1