具有中心对称结构的非负张量的谱半径

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1、2014年3月高等学校计算数学学报第36卷第1期具有中心对称结构的非负张量的谱半径木赵晓明杨庆之(南开大学数学科学学院／核心数学和组合数学实验室，天津300071)SPECTRALRADIUS0FAN0NNEGATIVETENS0RWITHCENTR0SYMMETRICSTR，UCTUREZhaoXiaomingYangQingzhi(SchoolofMathematicalSciencesandLPMC，NankaiUniversity，Tianjin300071)AbstractThematrixwithcentrosymmetricstructureisanimportan

2、tkindofstructuredmatriceswithmanyapplicationsinvariousphysicsandengineeringproblems．Theeigenvalueproblemforacentrosymmetricmatrixcanbereducedtotheothereigenvalueproblemsoflowerorder．Weintroducethecentrosymmet—ricstructuretothetensorfieldandfocusonthespectralradiusofthisparticulartensor．Thenwe

3、showthatpropertiesofcentrosymmetricmatricesholdtruefortensorssituation．Keywordscentrosymmetrictensor，eigenvalueproblem，Perron—Frobeniusthe—OremAMS(2000)subjectclassifications15A18，15A69中图法分类号022收稿日期：2011，02072014年3月高等学校计算数学学报591IntroductionForanumberofdecadessymmetricmatricesovertherealfieldh

4、avebeenstudiedintentlyasaclassofmatriceswhicharedefinedbythepropertyofbeingsymmetricabouttheirmaindiagong1．In[1]A．C．Aitkendefinesacentrosymmetricmatrixthroughthefollowingsquarematrix：0-．0101Definition1．1Ann×nmatrixBovertherealfieldiscentrosymmetricifBi，j=(JBJ)i，j=B+1～t，+1一j，for1i，Jn上’hecentro

5、symmetricmatrix18averyimportantkindO±structuredmatrices．Therearemanyapplicationsthatgeneratecentrosymmetricmatrices．Theyoccurnaturallyindigitalsignalprocessing[2]andwaveletanalysis[5，7]．ThePerron·Frobeniustheoremisafunda—mentalresultfornonnegativematrices．Ithasbeenwidelyusednotonlyinmathemati

6、csbutalsoinvariousfieldsofscienceandtechnology,suchaseconomics，operationalresearchandpagerankintheinternet；formoreinformationsee[11，8]．Atensorisamultidimensionalarray．Moreformally．anN—wayorNth—ordertensorisanelementofthetensorproductofNvectorspaces，eachofwhichhasitsowncoordinatesystem．Manyres

7、ultsformatricesstillbetruetotensors，suchasthePerron—Frobeniustheorem[3，13]．Fornonnegativetensors，thePerron-Frobeniustheoremisrelatedtomea-suringhigherorderconnectivityinlinkedobjects[9]andhypergraphs[4]．AfterNg，Qi，andZhou【10】gaveamethodtofind