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页数:8页
时间:2019-03-06
《上双对角阵moorepenrose广义逆的并行计算new》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、万方数据第5期华拳耨蓬大学学擐f垂然辩学驻)》b5垫QZ篁£旦垫璺艇:!望墅g!i!!些!缴型型!墼艘¥【墼彗::鲤!!蜜慰!型:!篓!A蛀{e捂lD:l糖甄§秘l《2瓣7)e硎缸07P黜蛆klCo啦)utatio娃oftheMoor伊Pe越oseInVerseofaBidiagonaLlMatr没融NG艇&o-z瓤ong(肌p州mem0,肌如emⅡ既甜,嚣n耵吼ind胁m耐洳z雠rsi蚍鼽口嘶m200062,删nn)Ab蘸r神缸Th蟊pap牲de哦制蚀p缸《碱∞芏np珏毫戢酶n《theMoo舱.致㈣k㈣ofabidia90n甜m舭m.Ad
2、ividea11dc叽quer“gorithmw舳舀ven.AnumencaJex啦ple8ndatheoreⅢaboutp8ralleIemciencywefepre∽nted.薹c∞7帮or豳:‰}e-轨啦∞孵洫㈣;躐轴;。n8重m缸r吣d知韬e8nd。onquer曲笋mhInCIJC肌mber.0151.2l:0241.6Documentcode;A上双对角阵Moore_penrose广义逆矗q并行计算方蔑孛(华末师范大学数学系,上海200062)摘要:研究耀一韩Ⅱ《努彝治之抟嚣法鞋计算童双对燕晦熬Mo。拎p翱瑚e广义逆。鞲时绘窭一个
3、数值恻予和一个关于并行效帮的定理.关键词:M00re-n蛆ro∞广义逆;上双对角阵;分商治之算法0IInroduction{f五主8赫∞口×稚∞珂pl娃檄8毛r政,氆簖l豇gMo潍P鞠lroseinve姆ecanbedenoted蟊sAt.Thj8uniquematr谴whichisde曲nted硝X8ati曲esfollrm舭ri](equations(A+denotes^’8co蝎ug疑如tr瓤印ose)AxA。A,xAx=x,Ax=(Ax)+,xA=(xA)+酗∞r争P强∞sein矬r辨越主s群通讫r昭毪巷8pp毡德£垂。珏8遮#ta
4、ti疵豳,sc耋船鹕8孰deB菇nee扣ing,8udl硒le聃t8quare8appr帜im从ion,singIllardi矗“eⅡt瑚anddi髓ren脚equatio焖,singul舯control,Markovch越ls8IIdi1Lp08edproblemsll~。There8remany溉portantalgori乇hm8computingtheMoore一}龟nroseiⅡ懈r搴es《ma乇rices,8黼h船Grev丑k赫拭orithm,触卜rank融otorizatioⅡalgoritllIll,svD础gorithm,C
5、linea岫即ithm,e地Ⅲ一.The8ealgorith瑚havedi雎remapplic蚺l、,e88pec魄Tll积kst。如eunce嬲illgprogre辅。fp射翻leleomp斌嘲,threse耵chof收稿日期:200&09基金壤基:国家鑫然辩学纂垒《1057l。6∞;华拳蜉范大学2黼年优秀撼圭疆究生培养基金作者简介:方麓中(197毒-),男,博士研究生.万方数据theparallel出90rithIll8g“8rapIddevelopment.Thepara工IeIcomputationofgeneralizedinve
6、rse8wasdiscllB8edin[5.12卜Inthisp印er,We而ude“withpar猷klcomputationofMoore_Penr0∞in、rer8eofabidiagoⅡ出matr.Ⅸ.Lem眦1【3lLetA∈Rm。“,thenwehaveorthogonalmatric船U∈R,。mandy∈R”o“suchthatUTAy=d1^0d20··,2··00···⋯d。1^一lO0drI(1)Iti8knownthatboth【,andycanbe画venbyHollseholdermatric明products.
7、Therearesomealgorithm8abouthawtogetthesematr岫【3】.Lemma2【1剐letA∈Rm。”.AccordingtoLemma1,there盯eorthogonalmatricesU∈Rm×mandy∈R“x“Bucht}latU7Ay=TwhereTi8abidiagondmatri】(.AndAt:yTtUT(2)AccordingtoLemm1,wecanchangem8tri)【Aintoabidianonalmatri】【,andthenWecomputeMoo睁Penro舱irⅣerse
8、ofmatr.ⅨT.ThlJBwec眦lgetM00re_Penro神im哪8eofmatri】cA抒omLemma2.Sohereweonlycon8idert0compute
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