一种同时求多项式所有零点及其重数的混合并行策略.pdfVIP

CHINESE JoURNAL Dec．2014 Vb1．31NO．6 oF ENGINEERIN G M ATHEM ATICS doff10．3969／j．issn．1005—3085．2014．06．012 ArticleID：1005—-3085(2014)06-0·903—-12 A M ixed ParallelStrategy forDeterm iningall Zerosand M ultiplicitiesofaPolynom ial丰 LIU Lan—dong， FU Yun—shan (DepartmentofMathematics，CollegeofSciences，ChinaUniversity ofMiningandTechnology,Beijing100083) Abstract：Inthispaper，anew mixedparalleliterativestrategyisdesignedtodeterminesimul— taneouslyallmultiplezerosandtheircorrespondingmultiplicitiesofapolynomia1． Thenew strategy isconsistedoftwo phases：therough calculation oneand the acceleratedcalculationone．In phaseone，alllow accuracy zerosandtheircorre- spondingmultiplicitiesarecomputedbyalocallysecond—orderconvergentmethod． In phasetwo，an acceleration oftheiterativeprocessisproposedandproved to bealocallyfourth—orderconvergence．Byusingthenew method，alllow accuracy zerosare accelerated．Numericalexperimentsaregiven tovalidatetheefficiency andsuperiorityofthenew strategy． Keywords：zerosofapolynomial；simultaneousmethod；multiplezeros；multiplicity；conver— gentorder Classification：AMS(2000)65H05 CLCnumber：O241．7 DOCtL1meritcode：A 1 Introduction M any problemsin appliedmathematicsandengineeringfieldsrequirethedeter— minationofthezerosofapolynomia1．Typically,theseproblemsoccuringeometric modeling，computerscience，robotics，signalprocessing，astronomy,finance，andSOon． A polynomialmodelcanbewrittenasfollows P扎()= +alz“一+ ···+an-1Z+an， aj∈C． (1) Among numerouszero—finding simultaneousmethods，oneofthemostefficient andfrequentlyusedmethodsisthewell-knownEnrlich-Aberthmet