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1、萬方數(shù)據(jù)第5期華拳耨蓬大學(xué)學(xué)擐f垂然辯學(xué)駐)》b5墊QZ篁£旦墊璺艇:!望墅g!i!!些!繳型型!墼艘¥【墼彗::鯉!!蜜慰!型:!簍!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沒融NG艇&o-z瓤ong(肌p州mem0,肌如emⅡ既甜,囂n耵吼ind脅m耐洳z讎rsi蚍鼽口嘶m200062,刪nn)Ab蘸r神缸Th蟊pap牲de哦制蝕p缸《堿∞芏np玨毫戢酶n《theMoo艙.致㈣k㈣ofabidia90n甜m舭m.Ad
2、ividea11dc嘰quer“gorithmw舳舀ven.AnumencaJex啦ple8ndatheoreⅢaboutp8ralleIemciencywefepre∽nted.薹c∞7幫or豳:‰}e-軌啦∞孵洫㈣;躐軸;。n8重m缸r吣d知韜e8nd。onquer曲筍mhInCIJC肌mber.0151.2l:0241.6Documentcode;A上雙對角陣Moore_penrose廣義逆矗q并行計算方蔑孛(華末師范大學(xué)數(shù)學(xué)系,上海200062)摘要:研究耀一韓Ⅱ《努彝治之摶囂法鞋計算童雙對燕晦熬Mo。拎p翱瑚e廣義逆。鞲時繪窶一個
3、數(shù)值惻予和一個關(guān)于并行效幫的定理.關(guān)鍵詞:M00re-n蛆ro∞廣義逆;上雙對角陣;分商治之算法0IInroduction{f五主8赫∞口×稚∞珂pl娃檄8毛r政,氆籪l豇gMo濰P鞠lroseinve姆ecanbedenoted蟊sAt.Thj8uniquematr譴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(nóng)爭P強∞sein矬r辨越主s群通訖r昭毪巷8pp氈德£垂。玨8遮#ta
4、ti疵豳,sc耋船鶘8孰deB菇nee扣ing,8udl硒le聃t8quare8appr幟im從ion,singIllardi?!癳Ⅱt瑚anddi髓ren腳equatio燜,singul舯control,Markovch越ls8IIdi1Lp08edproblemsll~。There8remany溉portantalgori乇hm8computingtheMoore一}龜nroseiⅡ懈r搴es《ma乇rices,8黼h船Grev丑k赫拭orithm,觸卜rank融otorizatioⅡalgoritllIll,svD礎(chǔ)gorithm,C
5、linea岫即ithm,e地Ⅲ一.The8ealgorith瑚havedi雎remapplic蚺l、,e88pec魄Tll積kst。如eunce嬲illgprogre輔。fp射翻leleomp斌嘲,threse耵chof收稿日期:200&09基金壤基:國家鑫然辯學(xué)纂壘《1057l。6∞;華拳蜉范大學(xué)2黼年優(yōu)秀撼圭疆究生培養(yǎng)基金作者簡介:方麓中(197毒-),男,博士研究生.萬方數(shù)據(jù)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眥1【3lLetA∈Rm?!?,thenwehaveorthogonalmatric船U∈R,。mandy∈R”o“suchthatUTAy=d1^0d20··,2··00···?d。1^一lO0drI(1)Iti8knownthatboth【,andycanbe畫venbyHollseholdermatric明products.
7、Therearesomealgorithm8abouthawtogetthesematr岫【3】.Lemma2【1剮letA∈Rm?!保瓵ccordingtoLemma1,there盯eorthogonalmatricesU∈Rm×mandy∈R“x“Bucht}latU7Ay=TwhereTi8abidiagondmatri】(.AndAt:yTtUT(2)AccordingtoLemm1,wecanchangem8tri)【Aintoabidianonalmatri】【,andthenWecomputeMoo睜Penro艙irⅣerse
8、ofmatr.ⅨT.ThlJBwec眥lgetM00re_Penro神im哪8eofmatri】cA抒omLemma2.Sohereweonlycon8idert0compute