ֻ27जֻ2௹, 2014୍4ᄅ ୡѯն࿐࿐Бč۽ϱĎ ൮ࢽᇏݓۚႪྮ॓௹़ࢂ , Apr. 2014 JOURNAL OF NINGBO UNIVERSITY ( NSEE ) ᆄࡾസႪྮ॓௹़၂֩ࢂ mᇗؓ࢘ၹሰ࿖ߌइᆔބܼၬ֥Euclidෘم *ޥתࢭ, ᖳࡹ૬ čୡѯն࿐ ࿐ჽ, ᆄࡾ ୡѯ 315211Ď ᅋေ: ০Ⴈ؟ཛൔEuclidෘم۳ԛਔ٤అၳmᇗؓ࢘ၹሰ࿖ߌइᆔ֥၂۱ྍෘم, ѩࡼھෘمܼᇀmᇗؓ࢘ၹሰ࿖ߌइᆔ֥ಕބMoore-Penrose, ࠣ۳ԛਔऎุ֥҄ᇧ. ܱՍ: mᇗؓ࢘ၹሰ࿖ߌइᆔ; ; ಕ; Moore-Penrose; Euclidෘم ᇏٳোݼ: ໓ངѓᆽ: A ໓ᅣщݼ: 1001-5132č2014Ď02-0101-05 A=f(R,",R)= ࿖ߌइᆔࠣఃܼᄝඔ࿐a࿐ބ۽ӱඌ1mn−1n−1n−1jm12mtm֩ਵთႋႨܼٗ, ၹՎฐษmᇗؓ࢘ၹሰ࿖ߌइ−1jt"a(d)⊗R, ∑∑∑j,"∏∏,s1mt=1ᆔఃྟᇉބႋႨཁ֤ޓႵсေ. гᆀ০Ⴈ؟ཛൔj=0j=0j=0t=1s=012m֥Euclidෘم۳ԛਔmᇗؓ࢘ၹሰ࿖ߌइᆔఃᇏ, ބܼၬ֥၂ᇕॹෘم, ֥၂۱ཁᇷหׄ൞f(x,",x)= 1mn−1n−1n−1jm12mtླყ༵ᆩ֡ھइᆔ൞ڎ٤అၳ. −1jt"a(d)x, ∑∑∑j,",∏∏,s∏1mഡR=DC൞၂۱٤అၳ֥ࠎЧؓ࢘ၹሰ࿖j=0j=0j=0t=1s=0t=1ttt12mߌइᆔ, ఃᇏ, ӫ؟ཛൔf(x,",x)ູmᇗؓ࢘ၹሰ࿖ߌइᆔA1mD=diag(dd,"d),tt,1t,2,nt֥іൕ؟ཛൔ. 0100"0⎡⎤: ⎢⎥nt0010"0ntddd=1,t1,2",m, t=1,",m. t∏,st,0C="""""",s=0tΔ=diag(σσ,"σ), 0000"1tt,1t,2,nt⎢⎥1000"0⎣⎦ఃᇏ, σડቀၛ༯֥־܄ൔ: σ=(d/d)⋅ n×nttt,jt,j+1tt,jttt [1]σ,1≤j≤nσ=σ=1,"m. קၬ1 گඔთഈ1۱nn"n×nn" t,jttt,n+1t,112m12ttω=exp(2πi/n)ູnՑЧჰֆ໊۴, F= nइᆔAડቀA(R⊗R⊗"⊗R)=(R⊗R⊗ ttm12m12(i−1)(j−1)tt(F)൞Fourierइᆔ, ఃᇏF=ω/n, ⊗R)A, ᄵӫAູmᇗؓ࢘ၹሰ࿖ߌइᆔ. Ⴈi,jni,jtmtttttmn,",n1m1≤i,j≤n,t=1,2,",m. SCіൕگඔთഈ෮Ⴕა⊗Rॖࢌߐ֥mᇗtttR,",Rt1mt=1 [1]n"n1mႄ1 ഡA=SCACIRC(a,",a, ؓ࢘ၹሰ࿖ߌइᆔ. R0,"0j,"1mn,",nn1mt",a)∈SC, ᄵ n−1,"n−1R,",Rn1m1mtႮ໓ང[1]ॖᆩ, Rࠞཬ؟ཛൔູx−d mmmmt∏t,jt−1j=1t(ΔF)A(ΔF)= ⊗t⊗t⊗t⊗tt=1=1t=1=1(t=1,",m). ٚьఏ, ࠺൮ྛჭູ(a", 0,",0n−1n−11mdiag(f(d,",d),",f(dω,",dω)), ma,",a)֥mᇗؓ࢘ၹሰ࿖ߌइᆔູj"jn−,"n−11,m1mn,",n1mn"nѩ, A∈SC֒ࣇ֒ 1mR,",RA1m=SCACIRC(a,,a,",a), ᄵRR0,"0j,"jn−1,"n−1mmmm1m1m−1(ΔF)A(ΔF), Aॖіൕູ: ⊗t⊗t⊗t⊗tt=1=1t=1=1 *
102 ୡѯն࿐࿐Бč۽ϱĎ 2014 mm൞ؓ࢘इᆔ−1. 0,",0)(ΔF). ⊗t⊗t [1]n"n1mt=1=1ႄ2 ഡA=SCACIRC(a,",a, R0,"0j,",1ms+n,",n1mn,",nၹՎ, ೂݔR൞ᆞ֥ܿ, ᄵA=A∈SC. 1mtR,",R"1m,a)∈SC, ᄵA֥หᆘᆴູ: n−1,"n−1R,",R1m1mii1mλ=f(dω,",dω)= ii"i11mm1 ᇶေࢲݔ 12mn−1n−1n−1j12mt−1ijttn"n1m"(d)a(dω), ק2 ഡA=SCACIRC(a",a, ∑∑∑∏∏t,sj,j",j∏tt12mR0,",0j,",1mj=0j=0j=0t=1s=0t=112mn,",n1m",a)∈SC, g(x)൞R֥ࠞཬ؟ཛn−1,",n−1R,,RRt1mti=0,",n−1,t=1,",m. tti1ൔ, t=1,",, ᄵg(x),",g(x)֥۴ቆ(dω, RR11n1mt2n−1nittmఃᇏ, d,dω,dω,",dω൞x−d,(t= ",dω), i=0,",n−1,t=1,",ᇏႵk۱ቆ൞ttttttt∏t,jmmtttj=1tf(x,",x)֥ਬ֥ׄԉေ่ࡱ൞rankA=nn" 1m121,",m)֥n۱҂֥۴. tn−k, ఃᇏ, f(x,",x)൞A֥іൕ؟ཛൔ. m1m [1]n,",n1mႄ3 ഡA,B∈SC, ᄵAB=BA∈ R,",R1mᆣૼ Ⴎႄ1ॖᆩ, n,",n−1n,",n1m1mmmmmSC, A٤అၳ, ᄵA∈SC. R,",RR,",R−11m1m(ΔF)A(ΔF)=D, n"n⊗t⊗t⊗t⊗t1mഡA=SCACIRC(a,a,,a) t=1=1t=1=1RR0,",0j,",jn−1,",n−11mn−1n−11m൞گඔთഈ֥mᇗؓ࢘ၹሰ࿖ߌइᆔ, ᄵA௶ູ: ఃᇏ, D=diag(f(d,d,",d),",f(dω,",dω). 12m111ntσ(A)={λ=0,"n−1,t=1,"m}. i"itt2n−1n1mttd,dω,dω,",dω൞g(x)=x−d, tttttttR∏t,jtഡ֒λ=0ൈ, T=0; ֒λ≠0ൈ, j=1tii"ii"iii"i12m1m12m(t=1,",m)֥n۱҂֥۴, ෮ၛ, T=1/λ,=0,,n−1,t=1,",m. ti",ii",itt1m1mmmmmೂݔ A(ΔF)=(ΔF)D. ⊗t⊗t⊗t⊗tmmt=1=1t=1=1B=(ΔF)diag(T,"⊗t⊗t0"0mmt=1=1ႮႿΔF൞٤అၳ֥, ၹՎ, ⊗t⊗tmmt=1=1−1mmT,",T(ΔF), i"i(n−1)"(n−1)⊗t⊗1m1mrankA=rankA(ΔF)= t=1=1⊗t⊗tt=1=1sᄵႮ໓ངmm[1]ॖᆩB൞A֥௶, ࠧB=A. rank(ΔF)D=rankD=D, n,",n1m⊗t⊗tႮႿSCᇏ֥ၩइᆔAႵᆷѓ1, ܣR,",Rt=1=11msA֥௶A္൞A֥ಕ. ࣉ၂҄, ೂݔR൞ᆞᇏ҂ູ0֥۱ඔ. ts+ii1m֥ܿ, ᄵA=A. ૌླေೂ༯֥ק. ೂݔg(x),",g(x)֥۴ቆ(dω,",dω)RR11mm1m [1]n"ni1m1ק1 ഡA=SCACIRC(a",a, ᇏႵk۱ቆ൞f(x,",x)֥ਬׄ, ࠧႵk۱f(dω, R0,",0j,",1m111mn,",nii1mm1",a)∈SC൞၂۱అၳ֥mᇗؓ࢘ၹ",dω)=0, ᄵႵnn"n−k۱f(dω,", n−1,",n−1R,",Rmm12m111m1m#sn,",ni1mmሰ࿖ߌइᆔ, ᄵA=A∈SC, ҂ാ၂Ϯྟ, dω)≠0, ၹՎႵrankA=nn"n−k. R,",Rmm12m1mࡌഡ: ّᆭ, ೂݔrankA=nn"n−k, ᄵDᇏႵ12mmmii1mnn"n−k۱f(dω,",dω)≠0. ၹՎDᇏႵ12m11mmA=(ΔF)diag(fd,"d)," ⊗t⊗t1mii1mt=1=1k۱f(dω,",dω)=0, ࠧg(x),",g(x)֥11mmRR1mik−1m1iif(dω,",dω),",f(dω,", 1m11mm11۴ቆ(dω,",dω)ᇏႵk۱ቆ൞f(x,",x)֥11mm1mmmk−1−1mਬׄ. ω),0,",0)(ΔF) mm⊗t⊗tn"nt=1=11mં1 ഡA=SCACIRC(a,",a, R0,"0j,"1mii1mఃᇏ, f(dω,,dω)≠0,i=0,",k−1,t=1,", n,",n1m11mmtt",a)∈SC, ᄵA٤అၳ֥ԉေ่ࡱ൞ n−1,"n−1R,",R1m1mnnm, ᄵ, 1mnn1mmm(f(x,,x),x−d,,x−d)=1, ః 1∏,j∏,j11m#sA=A=(ΔF=j=1)diag(," 1m⊗t⊗tnf(d,",d)tt=1=11mntᇏ, f(x,",x)൞A֥іൕ؟ཛൔ, x−d൞ 1m∏,jtj=1,",, tiik−1k−1mf(dω,",dω)f(dω,,dω)11mm11mmR֥ࠞཬ؟ཛൔ(t=1,",m). t
ֻ2௹ ޥתࢭ, ֩: mᇗؓ࢘ၹሰ࿖ߌइᆔބܼၬ֥Euclidෘم 103 iin"n1m1mקu'(dω,",dω), 0≤i≤n−1,t=1,",m. ෮ၛ, 3 ഡA=SCACIRC(a,",a, 11mmttR0,"0j,"1mn,",n'1m",a)∈SC൞1۱٤అၳ֥mᇗؓ࢘u(R,,R)=u(R,",R). n−1,"n−1R,",R1m1m1mၹሰ࿖ߌइᆔ, A֥іൕ؟ཛൔູf(x,",x), 1mႻႮႿ, mmᄵթᄝՑඔቋ֥֮؟ཛൔu(x,",x)ડቀ: 1mB=u(R,R,,R)(ΔF)diag(u(d,", 12m⊗t⊗t11iit=1=11mu(dω,",dω)=, 11mmii1miin−1mf(dω,",dω)d),",u(dω,",dω),",u(dω,", 11mmm1111mmmmi=0,1,,n−1,t=1,2,,, n−1−1ttmω)(ΔF)=(ΔF)⋅ m⊗t⊗t⊗t⊗tntt=1=1t=1=1n−1tఃᇏ, R֥หᆘ؟ཛൔູx−d, A= t∏t,jtj=1tdiag(,", i1imf(d,",d)f(dω,",dω)n,",n1m1m11mmu(R,R,",R)∈SC. 12mR,",R1mmm1−1",)ΔF, ᆣૼ ႮႿA൞၂۱٤అၳ֥mᇗؓ࢘ၹሰttn−1n−1⊗⊗1mf(dω,",dωt=1=111mm࿖ߌइᆔ, Ⴎં1ॖᆩ, ၹՎ, BA=I. nn1mnn1m(f(x,",x),x−d,",x−d)=1, ႮႿB=u(R,",R)൞f(R,",R)֥, ᄵ1m∏,j∏,j1m1m1mj=j=11m؟ཛൔu'(x)ॖႨEuclidෘم֤. Ⴟ൞թᄝu',v,v,",v∈C[x,x,",x]ડቀ: 12m12mູࡥ߄࠹ෘ, ഡf(x,",x)༢ඔ൞aa≠0, 1mn1n2u'f(x,",x)+v(x−d)+v(x− f'(x,",x)=f(x,,x)/a, ᄵf(x,",x)= 1m1∏,j21m1m1j=11af'(x,,x),f'(x,"֥,x)൮ཛ༢ඔ൞1. 1mnn2mnn"nm1mdק4 ഡA=SCACIRC(a,",a, )+"+v(x−d)=1, ∏2,R0,"0j,",jm,j2mm=1n,",n2m1m",a)∈SC൞၂۱అၳ֥mᇗؓ࢘ၹn−1,",n−1R,",R1m1mఃᇏ, C[x,x,",x]ູگඔთഈ؟ჭ؟ཛൔߌ. 12mሰ࿖ߌइᆔ, A֥іൕ؟ཛൔູf(x,",x), ࡌ1mႨRٳљսูഈൔᇏ֥x, ၹູ, ttഡAႵk۱٤ਬหᆘᆴ, ҂ാ၂Ϯྟ, ॖഡg(x), R1ntin1t",g(x)֥k,k+1,",nn"n−1۱۴ቆ(dω, R−dI=0,t=1,",m, R12m11∏,jnmttij=1iimt1m",dω)֤f(dω,",dω)=0, ѩd,dω, mm11mmtttnႿ൞, t2n−1nttdω,",dω൞g(x)=x−d,t=1,"m֥ttttR∏,jtu'(R,R,",R)f(R,R,",R)=I. 12m12mntj=1tഡmu(x,x,",x)ູՑඔቋ֥֮؟ჭ؟ཛൔ12miit1۴. g(x,x,",x)=(x−dω), ఃᇏ(dω, 112m∏t11ડቀ: t=1'iu(x,xm,",x)−u(x,x,",x)∈ 12m12m",dω)൞g(x),",g(x)֥0,1,",k−1۱۴ቆ, mmRR1mmG(x,x,",x), RR"R12m12miit1g(x,",x)=(x−dω), ఃᇏ(dω,", 21m∏t11ఃᇏt=1, G(x,,",x)קၬູડቀ֒x=d, RR"R12m1112min−n−m2dω)൞g(x),",g(x)֥k,k+1,",nn"n−1dω,,dω;x=d,dω,,dω;";xd, mmRR12m1111222222mm1mn−1mdω,",dωൈG(x,,",x)=0֥Ց۱۴ቆ, f(x,,x)=f(x,",x)g(x,,x), mmmmRR"R12m111m2112mඔቋ֥֮൮၂؟ჭ؟ཛൔ, ࠧؓg(x),",g(x)ᄵթᄝ1۱؟ཛൔu(x,",x)ડቀ: RR11m1mii1miiiimm֥nn"n۱۴ቆ(dω,",dω)i=1,",n,t= u(dω,",dω)=1/f(dω,",dω), 12m11mmtt111mm111mmii1m1,",mनႵG(dω,",dω)=0, ఃᇏ, u(x,",x)=u(x,",x)g(x,,x), ᄵ: RR"R11mm12mm1m2+ૌӫG(x,,",x)ູگඔთഈ؟ჭ؟ཛA=u(R,R,",R). RR"R12m12m12mൔߌC[x,x,",x]֥ႮG(x,x,",x)ളӮᆣૼ ႮႿ, 12mRR"R12m12mnn−1tt֥མᆴ. itx−d(x−dω),=1,",m, ∏t,j∏nttttiniij=1i=0tt1mttၹູ(dω)−d=0, u(dω,",dω)= tt∏t,j11mmtႮg(x,",x),g(x,",x)קၬॖ֤: j=111m21mt
104 ୡѯն࿐࿐Бč۽ϱĎ 2014 ntn(g(x,",x),g(x,",x)=1. t11m21mx−d, ∏t,jtj=1tႻႮ่ࡱॖᆩ: ࠹ෘԛG(x,x,",x). r(x,x,",x)= RR"R12m−112m(g(x,",x),f(x,",x)=1, 12m11m1mG(x,x,",x), r(x,",x)=f(x,,x), RR"R12m01m1Ⴟ൞, (g(x,,x),f(x,,x)=1. 12m1111u(x,",x)=0, u(x,",x)=1, t=1,",m. −11m01mၹՎ, թᄝu(x,",x),v(x,",x)ડቀ: 21m1m҄ᇧ2 ০Ⴈ؟ჭ؟ཛൔ֥Ԣم, Ⴎ༯ൔ: u(x,",x)f(x,,x)+ 21m11r(x,",x)=r(x,",x)− i+11mi−11mv(x,,x)g(x,",x)=1. 11mii1mq(x,",x)r(x,,x), i1mim֒(x,x,",x)=(dω,,dω)൞g(x),", 12m11R1iiෘԛq(x,",x),r(x,",x),i=0,1,",m. 1mi1mi+11mg(x)֥0,1,",k−1۱۴ቆൈ, g(dω,",dω)= R111mmmiim҄ᇧ3 r(x,",x)֥൮ཌྷ༢ඔ൞c, : i+11mi+10, ෮ၛ, u(dω,,dω)f(dω,,dω)=1. 211mm111mmr(x,",x)←r(x,",x)/c,i=0,1,"m. i+11mi+11mi+1u(x,",x)−u(x,",x)∈g(x,",x), 11m21m11҄ᇧ4 Ⴎ༯ൔ: ෮ၛھקᇏu(x,",x)֥թᄝྟ֤ၛᆣૼ, ၹ11mu(x,",x)=(u(x,",x)− i+11mi−11mՎ, u(x,",x)=u(x,,x)g(x,",x). 1m21mii1mq(x,,x)u(x,,x)/c, imimi+1֒(dω,",dω)൞g(x),",g(x)֥k, 11mmRR1mෘԛu(x,",x), ሇ҄ᇧ2; i+11mk+1,",n"n−1۱۴ቆൈ, 12mii҄ᇧ5 ೂݔr(x,",x)=1,u(x,",x)൞1mk1mk1mu(dω,",dω)=0. 11mm−1−1iiA֥іൕ؟ཛൔ, ᄵA=u(R,R,",R); ڎᄵ, 1mk12֒(dω,",dω)൞g(x),",g(x)֥0,1, 11mmRR1mr(x,",x)=0, ᄵr(x,",x)൞f(x,",x)ބk1mk−11m1m",k−1۱۴ቆൈ, iiiiG(x,x,",x)ቋն܄ၹൔ. : RR"R12mu(dω,",dω)=u(dω,",dω)⋅ 12m11mm111mmr(x,x,,x)=r(x,x,",x), 1m12mk−112mg(dω,,dω)=g(dω,,dω)/ 211mm211mmir(x,x,",x), −112mf(dω,,d)=1/f(d,",d), 111mm11mmડቀ: , mmr(x,x,",x)r(x,x,",x)= −112mk−112mB=u(R,R,",R)(ΔF)diag(u(d,, 12m⊗t⊗t1G(x,x,",x), t=1=1RR"R12m12miin−1m{r(x,x,,x)−f(x,x,",x)r(x, d),",u(dω,",dω),",u(dω,", 01212mk−11m1111mmmmx,",x}∈r(x,x,,x), m−n−1−1mω)(ΔF)=(ΔF)⋅ m⊗t⊗t⊗t⊗tu(x,x,,x)=0,u(x,x,",x)=1, −112012mt=1=1t=1=1ሇ҄ᇧ2; diag(,," f(d,",d)f(dω,",dω)҄ᇧ6 ၂ᆰ࠹ෘ, ᆰ֞ԛགྷr(x,",x)=1,1m1mk1mmmᄵu(x,",x)ડቀ{u(x,",x)−u(x,,x)r(x, 11m1mkm−1,0,",0)(ΔF). ttk−1k−1⊗⊗#1m",x)}∈G(x,,x)൞A֥іൕ؟ཛൔ, f(dω,",dω)t=1=111mmmR"R1m12m#+ၹՎA=u(R,R,",R). ࣉ၂҄ॖᆩ, ೂݔR൞Ⴎק1ॖᆩ, B=u(R,R,",R)A. 12mt12m+#ᆞ֥ܿ, ᄵA=A=u(R,R,",R). 12m2 mᇗؓ࢘ၹሰ࿖ߌइᆔބܼၬ֥ෘم 3 ෘم۽ቔਈ ሸభ෮ඍ, ॖ֤֞mᇗؓ࢘ၹሰ࿖ߌइᆔ֥ೂݔmᇗؓ࢘ၹሰ࿖ߌइᆔ൞٤అၳ֥, ۽aಕބMoore-Penrose֥ෘمೂ༯. n"n1mቔਈॖٳູਆ҆ٳ. ࡌഡmᇗؓ࢘ၹሰ࿖ߌइᆔ҄ᇧ1 ႮA=SCACIRC(a,,a,", RR0,"0j,"j1mA֥ࢨඔ൞nn"n, ᄵdeg(f(x))=nn"n−m, a)֤֞: 12m12mn−1,"n−11m൮༵؟ჭ؟ཛൔԢم֥۽ቔਈູ: f(x,",x)= 1mn−1n−1n−1jm12mtr(x,",x)=r(x,",x)− i+11mi−11m−1jt"a(d)x, ∑∑∑j,",∏∏,s∏1mq(x,",x)r(x,,x), j=0j=0j=0i1mimt=1s=0t=112m
ֻ2௹ ޥתࢭ, ֩: mᇗؓ࢘ၹሰ࿖ߌइᆔބܼၬ֥Euclidෘم 105 r(x,",x)←r(x,",x)/c,i=0,1,",m. 4 ෘمॖྛྟ i+11mi+11mi+1ཁಖ, ؟ჭ؟ཛൔԢم҂ӑݖnn"n−mՑ. 12mҕॉ໓ང[5-6]ࢺകਔMathematicaaMaple֩ೂݔᆺ࠹ෘnn"n−mՑ, ᄵdeg(q(x,",x))= 12mi1mೈࡱીႵൌགྷ֥؟ჭ؟ཛൔԢمᄎෘ, ط০Ⴈഡm, q(x,",x),r(x,",x)൮ཛ༢ඔ൞1, Ⴟ൞ i1mi1m࠹֥թԥࢲܒࠣ؟ཛൔ֥ᄎෘି٤ӈಸၞൌགྷ, n−1n−1n−112m؟ჭ؟ཛൔԢم۽ቔਈູ2"ii"i, ҂ ∑∑∑ᄎෘ؇٤ӈॹ. гᆀᄝՎൌགྷਔ؟ჭ؟ཛൔ֥12mi=1i=1i=112mᄎෘ, ᄜ০Ⴈֻ҆ٳෘم, ္ࣼൌགྷਔmᇗؓ࢘ӑݖ2nn"n, ೂݔ࠹ෘഒႿnn"n−mՑ, ཁ12m12mၹሰ࿖ߌइᆔބܼၬ֥ෘم. ಖdeg(q(x,",x));m, ᄵླေࡥ߄؟ཛൔԢمi1m֥Ցඔ. Վ҆ٳ۽ቔਈ҂ӑݖ2nn"n. 12mҕॉ໓ང: ఃՑ, ษં؟ཛൔӰم۽ቔਈູ: [1] ࡾᅸਟ. ܼၬ࿖ߌइᆔࠣఃႋႨ[D]. ༆ν: ༆νሰ॓ն࿐, 2003. u(x,",x)=(u(x,",x)−q(x,",x)⋅ i+11mi−11mi1m[2] ࡾᅸਟ, ਾဝ. ᇂߐၹሰ࿖ߌइᆔބܼၬ֥u(x,",x)/c,i=0,1,". imi+Euclidෘم[J]. ༆νሰ॓ն࿐࿐Б: ሱಖ॓࿐ϱ, Ⴎෘمॖᆩ, ؟ཛൔӰم҂ӑݖnn"n−m12m2004, 31(1):148-152. Ց. ೂݔ࠹ෘnn"n−mՑ, ᄵdeg(q(x,", 12mi1[3] ࡾᅸਟ, ွౝ, ۚൾ. Ⴖ࿖ߌइᆔބܼၬ֥x))=m, q(x,,x),r(x,",x)൮ཛ༢ඔ൞ mimi1mEuclidෘم[J]. ۽ӱඔ࿐࿐Б, 2004, 21(2):227-232. n−1n−1n−112m[4] Jiang Zhaolin, Ye Liuqing, Deng Fang’an. The explicit 1, ᄵ؟ჭ؟ཛൔԢم۽ቔਈູ2"ii"i, ∑∑∑12mi=1i=1i=112mexpressions of levelcirculant matrices and −k(r,r,",r)12ktheir some properties[J]. Cheinese Quarterly Journal of ҂ӑݖ2nn"n, ೂݔ࠹ෘഒႿnn"n−mՑ, 12m12mMathematics, 1998, 13(2):91-96. ھ҆ٳӰم۽ቔਈ҂ӑݖ2nn"n, ၹՎሹ۽ቔ12m[5] ٚ໓ѯ. ॖ൪߄ژݼᄎෘ༢VSCS֥ഡ࠹აൌགྷ[J]. ਈ҂ӑݖ4nn"n. 12m࠹ෘࠏ۽ӱ, 2003, 29(6):183-185. ֒mᇗؓ࢘ၹሰ࿖ߌइᆔ൞అၳ֥ൈ, ෘم[6] ٚ໓ѯ. ؟ჭ؟ཛൔ֥թԥࢲܒࠣඹᄵᄎෘ֥ൌགྷ[J]. ࠹ෘಕࠇᆀMoore-Penrose֥ሹ۽ቔਈ҂ӑݖ١ᆮۚࠎԤ॓࿐࿐Б, 2003, 19(3):257-260. 8nn"n. 12mEuclid Algorithm for Finding Inverse and Generalized Inverse of m Multiplicity Diagonal Factor Circulant Matrix *HOU Dong-jie, CEN Jian-miao ( Faculty of Science, Ningbo University, Ningbo 315211, China ) Abstract: A new algorithm for finding the inverse of a nonsingular m multiplicity diagonal factor circulant matrix is presented using the Euclid algorithm of polynomial. The presented algorithm is extended to compute the Moore-Penrose inverse of a singular m multiplicity diagonal factor circulant matrix. The steps in derivation are given in detail. Key words: m multiplicity diagonally factor circulant matrix; inverse; group inverse; Moore-Penrose inverse; Euclid algorithm čᄳщࠠ ᅣ৫Ď
