广义对角占优矩阵和广义α.对角占优矩阵的判定

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1、AbstractGener出izeddi雒’0na

2、lydomiIlantmatrb(is丽delyusedinm锄ly舭eas．TbdeterIIlinewetheramatri】(isageneralizeddiagonallydominammatrixhalscomp盯ativelyhighertheoreticalv甜ueandpracticalbackground．Inrecentye缸s，thisproblemhasattractedlotsofrese盯chers’attention，andtheyhaⅣeobtained

3、ma∞7achieveInentsinthisregard．Withthedepthandra．ngeincreasing，generaLlizeda-diagpn出lydominantmatri)【whicllisbasedongeneralizeddiagon出1ydominantmatriXisra勰ed．TheyhaⅣema舳lysimilarpropertiesandequiv出encerelation．Thatistosa矾amatr仅isageneralizeddiagona．1lydominammatrb(ifand01

4、1lyifitisageneraUzedQ—diagonallydominantmatri)(．SoifWewa砒todeterminewhetheramatr政isageneraliZeddiagon甜lydominantmatri)【，wecanfirstlydeterminewetheritisageneralizedQ—diagon甜lydoIIlinantmatr政ornot．Thisisanewmethodtodeter而newetheramatri)(isageneralizeddiagonallydominaLIltma

5、tr仅．BecausethecloseconnectionofgeneraJlizeddiagonallydominantmatrb(andgeneral-izeda-diagonallydominantmatr政，itleadstoin．depthstudyonpropertiesaJldcriteriasofgeneralizeda-diagonallydominantmatrix．ItoH-erstheoreticalfundamentaltomatr仅theoryandcomputationaLlmathematicsandso

6、on．Tbjudge、Ⅳetheramatri)【isagene卜alizeda-diagonallydomin龇1tmatrb【ornotistofindapositiVediagonallymatr仅andapositive肌II】【bersuchthato越Izl>aa)∑1％k，Ⅵ∈Ⅳ．J≠iFindingthepositivematri)(andnumberha、retwomethods，theyaredirectmethodanditerativemethod．Int11ispaperwemainlydiscussthedi

7、rectmethod．ThispaperismainlybasedonthepropertiesaJldcriteriasofgeneralizeddiagonallydominantmatr没togueSsaJldpro、rethepropertiesaJldcriteriasofgeneralized乜一diagonalllyIII一1+％～s，0∑傅AbstractdoIIlinantmatri)(．ItprovidesnewmethodsofcriteriasofgeneraLlizeddiagonalllydomillantm

8、atri)(．W．ewill酉Vesomenumericalex锄plestopro、，ethemethods’signi6cance．There盯ethreech印tersinthisdissertation．Inthe6rstchapter，weintroducethestudyV甜ueaJldbackgroundofgeneraJizeddiagonallydominantmatr政．Inthesecondchapter，Ⅵ伧introducethede矗nitionandsyⅡlb01swhichwiUbeusedinthisp

9、aper．Atthesametime，we西vesomeclassicalcritiriasofgenera血zeddiagonallydo面na肛tmatr政andsomeequiValencetheor