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一类广义Bezout矩阵的研究.pdf

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AdvancesinAppliedMathematics应用数学进展2014398-103PublishedOnlineMay2014inHans.http://www.hanspub.org/journal/aamhttp://dx.doi.org/10.12677/aam.2014.32015StudyonaGeneralizedBezoutMatrixJingpengSun1HuazhangWu12*HaishengLi1LouChen11SchoolofMathematicalSciencesAnhuiUniversityHefei2KeyLaboratoryofIntelligentComputingandSignalProcessingMinistryofEducationAnhuiUniversityHefeiEmail:1946179973@qq.com*wuhz@ahu.edu.cnReceived:Mar.20th2014;revised:Apr.17th2014;accepted:Apr.24th2014Copyright©2014byauthorsandHansPublishersInc.ThisworkislicensedundertheCreativeCommonsAttributionInternationalLicense(CCBY).http://creativecommons.org/licenses/by/4.0/Abstractα(n)=±ni−i≤≤Thebases{i(zz)(11)(z)}(0in)ofthepolynomiallinearspacen+1[z]arecon-structedbythebilineartransformationfunction.GeneralizedBezoutmatricesundertwodifferentbasesareinvestigated.BythegeneratingfunctionsofBezoutmatricesafastalgorithmformulaanditscorrespondingtriangulardecompositionfortheelementsofthistypeofBezoutmatrixaregiven.Theformulashowsthatthecostofthealgorithmisο(n2).ConnectionbetweentwoBezoutmatricesunderdifferentbasesisdiscussed.Finallytwonumericalexamplesaregiventodemon-stratethevalidityofthetheory.KeywordsBilinearTransformationFunctionPolynomialBasisBezoutMatrixTriangularDecomposition一类广义Bezout矩阵的研究孙井鹏1吴化璋12*李海昇1陈楼11安徽大学数学科学学院合肥2安徽大学教育部智能计算与信号过程重