1、QRE p A+00986096v1008712011 M1023 KKK111QRE p A+:B5w :M| A Zu AH=AHQR( P M) 1 p Hn+b1555 A(inM L+),QRZE p n+b Aq“gr900900crg:mm“bi:mm T b2 EEE 2.1 L L L Aq“gr900900crg:mm“ :mm T “ AbA 900900v b matlaB P“A=zeros(900,900)“ 3900900 , bv.mmq sYiaj 3 “ Ai|Ai.matqLbA L900 A 900 L+ V PQRZE pb/ 8 Eb2.2 QR E
2、EEQR E X B nM+ A /MA = Q1R1;A1 = R1Q1A1 = Q2R2;A2 = R2Q21Ak = Qk+1Rk+1;Ak+1 = Rk+1Qk+1Qi Ri V I bAi+1 = QTi+1(Qi+1Ri+1)Qi+1 = QTi+1AiQi+1Ai+1AiM M+bi!1 HAiL/ t ,bB VAQRK ( Bd ,) VTA+b ?C / Z u T AHAH =2666666664a11 a12 a13 : a1n1 a1na21 a22 a23 : a2n1 a2n0 a32 a33 a34 : : : :0 0 : : an;n1 ann3777777
3、775(1)AHQRV V Z u TMbQR Es LCB| AM Z u AH,=N Z u AHQR TbB| AM Z u AH MAHA M+ w :M(M)W% = Z u AHQRi sQ R 7 MrMrT9W% QR EkQ HjAi+1;ijjAi;ij+jAi+1;i+1j 9K 6A #K-L AH* 6r) 1,XQRE GAi=QiRiAi+1=RiQiEQRE,X2zk$C2z,X?-L AnEgAn,X?20A-L ,X(MUA-L NoYes43/c*QRE“A,X(MU/cm1:(QRE p +) Ew :M|A Z u AH LC/ VA1 = H1AH1
4、A2 = H2A1H2An2 = Hn2An3Hn2H1aH2 :H126666664a11a21a31.an137777775=26666664a011a0210.037777775(2)3H226666666664a012a022a032a042.a0n237777777775=26666666664a0012a0022a00320.037777777775(3) /w : HiNf bHi “ | -Ai1i LC /MHi266666666666666664a01ia02ia03ia0iiai+1;iai+2;i.a0ni377777777777777775=2666666666666
5、66664a001ia002ia003ia00iia00i+1;i0.0377777777777777775(4) VAi1 |ni _ !x = a0i+1;i;a0i+2;i; ;a0niT|fi = k!xk2;n-i_ !e = 1;0;0; ;0T/! =!x fi!ek!x fi!e k2 (ni)(ni)w : H0i,| Hi =“Iii 00 H0i#(5)Hib LC:Ai = HiAi1Hi|NGQVi = 1i = n2 Tn-2Q Z u AH, O AM bf (function AH=A-to-AHessenberg(A,n) m m= Ub4i=n-2?XEn-
6、i4,Xwi G*wiXE(n-i)*(n-i),XH(n-i)*(n-i)=H(n-i)*(n-i)kHiAi=Hi*Ai-1*HiA-L Ai-1AiEg#K-L AH*B9K 6A-L , 6#K-L AHm2:w :M| A Z u AH E2.4 MMM L L LCCCBBBQQQrrrQR Xw :M| A Z u AH.BQQR7M M LCr LC/VG(n1;n; n1)G(n2;n1; n1)G(1;2; 1)AH = RG(i1;i; i1) bVrAH = QRQ = G(1;2; 1)T G(n2;n1; n1)TG(n1;n; n1)T RAHnew = RQ =
7、 RG(1;2; 1)T G(n2;n1; n1)TG(n1;n; n1)T5 T|Q si T * 9 7gdvb I nBrVbBV L= GQ|AH ii+1M(9 n-1QM) “ PAHi+1;i = 0b BVii+1Mb |ci = AHi;iqAH2i;i +AH2i+1;isi = AHi+1;iqAH2i;i +AH2i+1;i ii+1 MAH0i;j = ci AHi;j +si AHi+1;jAH0i+1;j = ci AHi+1;j si AHi;jj = 1;2; ;n.iV1n-1, V,5r LCQRsi Rb=VR Q AHnew = RQ = RG(1;2
8、; 1)T G(n2;n1; n1)TG(n1;n; n1)TrGQR i i+1 MbM R0j;i = ci Rj;i +si Rj;i+1R0j;i+1 = ci Rj;i+1 si Rj;ij = 1;2; ;n.iV1n-1, V,5r LCAHnew = RQVbN BQQRbf (AHnew=QR-iteration-once(AH,n) m m Ub3TTT functioneigenvalue;flag 1 = QR(A;n)f !accuracy = 103, |n=900,A2.1 f bTA Uflag1 = 9344b9 V9344QZ u QAH 0 V A+b T
9、BqCeigenvalue:matm A U 900+Vlv bVB 900+KvKl+b6XE 6G(i,i+1)AH-L 1i 1i+1 ,XSkAH i+1,i=01 r)A=QR.;G(1,2)T,G(2,3)TG(n,n-1)T9q R-L ,X1i 1i+11 r)Anew=RQ#K-L AHi=1:n-1k?-L RNOYESi=1:n-1NOYES43$/cr)q QREkAnew* 6r)AH-L ,X QREm3: Mr LCBQQR EV1:KvKl+Kv+11.9591 11.9591 11.9287 11.9287 11.8784 11.8783 11.8673 11.8668Kl+0.0615 0.1532 0.1532 0.2440 0.3050 0.3050 0.3942 0.394270 100 200 300 400 500 600 700 800 900024681012m4: A900+Vlv 8
