北航數(shù)值分析報告大作業(yè)第八題

實用文檔實用文檔標(biāo)準(zhǔn)標(biāo)準(zhǔn)北京航空航天大學(xué)數(shù)值分析大作業(yè)八學(xué)院名稱 自動化專業(yè)方向 控制工程學(xué)號 學(xué)生姓名 許陽 教師孫玉泉日期2014年11月年日．題目關(guān)于X,y,t,u,V,w的方程組(A.3)0.5cost+u+v+w一x=2.67t+0.5sinu+cosv+w-y=1.07(A.3)<… (A.3)0.5t+u+cosv+w一x=3.74t+0.5u+v+sinw一y=0.79以及關(guān)于4,t,u的二維數(shù)表（見表A-1）確定了一個二元函數(shù)4fx,y）。表A-1二維數(shù)表tzu00.40.81.21.620-0.5-0.340.140.942.063.50.2-0.42-0.5-0.260.31.182.380.4-0.18-0.5-0.5-0.180.461.420.60.22-0.34-0.58-0.5-0.10.620.80.78-0.02-0.5-0.66-0.5-0.021.01.50.46-0.26-0.66-0.74-0.51.試用數(shù)值方法求出f(x,y)在區(qū)域D={(X,y)10<x<0.8,0.5<y<1.5}上的近似表達(dá)式P(x,y)=￡工cxrys

rsi=0j=0要求p(x,y)以最小的k值達(dá)到以下的精度o=￡￡[f(x,y)一p(x,y)]2<10-7

ii iii=0j=0其中x=0.08i,y=0.5+0.05j。ii2.計算f(x*,y*),p(x*,y*)(i=1,2，…,8;j=1,2，…,5)的值，以觀察p(x,y)逼ijij近f(x,y)的效果，其中x*=0.1i,y*=0.5+0.2j。ij二．算法設(shè)計(一)總體思路1.題目要求p(x,j)=￡￡c不"對f(x,y)進(jìn)行擬合，可選用乘積型最小二乘rsi=0j=0TOC\o"1-5"\h\z擬合。(x,y)與f(x,y)的數(shù)表由方程組與表A-1得到。ii ii2.f(x*,y*)與1使用相同方法求得，p(x*,y*)由計算得出的p(x,y)直接帶入ij ij(x*,y*)求得。ij(二)算法實現(xiàn)1.(x,y)與f(x,y)的數(shù)表的獲得ii ii對區(qū)域D={(x,y)10<x<0.8,0.5<y<1.5}上的f(x,y)值可由方程組及二維數(shù)表得到。將區(qū)域D上的(x,y)分別回代于方程組(A.3)，成為關(guān)于t,u,v,w的4ii元非線性方程組，解出每個(x,y)對應(yīng)的t,u。再通過表A-1進(jìn)行插值近似，得ij到相應(yīng)的z值。對應(yīng)的z即為D區(qū)域上(x,y)對應(yīng)的f(x,y)。從而得到(x,y)ij ij ij與f(x,y)的數(shù)表。ii(1)4元非線性方程組求解(x,y)代入(43)后，原方程組變?yōu)殛P(guān)于t,u,v,w的4元非線性方程組。觀察到ii方程組中方程形式較為簡單，易于對變量t,u,v,w求偏導(dǎo)數(shù)，故而選用Newton法對方程組求解。計算方程組矩陣為：’0.5cost+u+v+w—x—2.67'iF(t,u,v,w)t+0.5sinu+cosF(t,u,v,w)… i…0.5t+u+cosv+w—x—3.74\t+0.5u+v+sinw—y—0.79)i計算方程組偏導(dǎo)數(shù)矩陣為:'-0.5sint111)10.5cosu11F(t,u,v,w)=0.51一sinv11v10.51coswJ迭代公式為：+<AA(kJAu(k)Av(k)(Aw(k)J，k=0,1,2,…,n其中乙一、t(k+1)u(k+1)v(k+1)Vw(k+1)J=t(k)u(k)v(k)vw(k),<AA(k] fAA(k「Au()為線性方程組F'(t(k),u(k),v(k),w(k))“"()=嚇(t(k),u(k),v(k),w(k))的解。Av(k) Av(k)vAw(k)/VAw(k),取max(lAt(k)I,IAu(k)|,|Av(k)|,|A段(k)|)/max(lt(k)I,Iu(k)|,|v(k)|,|故(k)|)<8為迭代終止條件。由表A-1觀察到t,u基本在(0,2)上，于是選取(t(0),u(0),v(0),段(0))=(1,1,1,1)為迭代初值。通過以上方法求得與(%,y)對應(yīng)的(t,u)。ij ijij(2)分片二元雙二次代數(shù)插值為保證代數(shù)插值的收斂性，應(yīng)采用分片低次插值。故此使用分片雙二次代數(shù)插值。t=0.2m,u=0.4n(m=0,1,...,5;n=0,1,...,5)m n給定(t,u)如滿足如下關(guān)系式：ijijt—0.1<t<t+0.1，1<m<4m ijm

u一0.2<u<u+0.2,1<n<4ijn則選擇(t,u)(k=m,m+1,m+2;r=n,n+1,n+2)為插值節(jié)點，相應(yīng)插值多項式p(t,u)=￡nE21(t)l(u)z(t,u)22ijij kijrijkrk=mr=n其中f用t一t .ij—q (k=m,m+1,m+2)kij t一tq=mkqq豐kl(u)工ijl(u)工ij-4j q(r=n,n+1,n+2)u—ukq如果t<0.3如果t<0.3或t>0.7ijij則上式取m=1或m=4；如果u<0.6或u>1.4，則ij ij取n=1或n=4。TOC\o"1-5"\h\z得到p(t,u)表達(dá)式后，直接帶入(t,u)，得到的值即為與(％,y)對應(yīng)的22ijij ijij ijf(x,y)。ij.乘積型最小二乘曲面擬合使用乘積型最小二乘擬合，根據(jù)k值不用，有基函數(shù)矩陣如下：b=%0：0… %k0?. ：，G=(?y0：… yk0?. ：1%0…%kiI[”…ykjI數(shù)表矩陣如下：TOC\o"1-5"\h\zfa,y)…f(%,y)

00 . 0jU= ： .?:〔f(%,y)…f(%,y)I

i0 ij記C=[c]，則系數(shù)c的表達(dá)式矩陣為：rs rsC=(BtB)-1BtUG(GtG)-1通過求解如下線性方程，即可得到系數(shù)矩陣C。(BTB)C(GTG)=BTUG.計算f(x*,y*),p(x*,y*)(i=1,2r,8;j=1,2r,5)的值ijijf(x*,y*)的計算與f(x,y)相同。將(x*,y*)代入原方程組，求解響應(yīng)(t*,u*)j ij ij ijij進(jìn)行分片雙二次插值求得f(x*,y*)。p(x*,y*)的計算則可以直接將(x*,y*)代入所ij ij ij求p(x,y)。三.Matlab源程序及結(jié)果牛頓法解非線性方程組子程序：function[t,u]=newt(x,y)t=1;u=1;v=1;w=1;ep=1e-12;k=1;N=100;while(k<N)F(1,1)=0.5*cos(t)+u+v+w-x-2.67;F(2,1)=t+0.5*sin(u)+v+w-y-1.07;F(3,1)=0.5*t+u+cos(v)+w-x-3.74;F(4,1)=t+0.5*u+v+sin(w)-y-0.79;dF=[-0.5*sin(t)111;10.5*cos(u)11;0.51-sin(v)1;10.51cos(w)];deltaX=ones(4,1);deltaX=dFA-1*(-1)*F;ifmax(abs(deltaX))/abs(x)<ept=t+deltaX(1,1);u=u+deltaX(2,1);v=v+deltaX(3,1);w=w+deltaX(4,1);break;endt=t+deltaX(1,1);u=u+deltaX(2,1);v=v+deltaX(3,1);w=w+deltaX(4,1);k=k+1;end分片雙二次代數(shù)插值子程序：functionf=p22(t,u)z=[-0.5-0.340.140.942.063.5;-0.42-0.5-0.260.31.182.38;-0.18-0.5-0.5-0.180.461.42;0.22-0.34-0.58-0.5-0.10.62;0.78-0.02-0.5-0.66-0.5-0.02;1.50.46-0.26-0.66-0.74-0.5];if(t<=0.3)i=1;endif(t>0.3&&t<=0.5)i=2;endif(t>0.5&&t<=0.7)i=3;endif(t>0.7)i=4;endifu<=0.6j=1;endifu>0.6&&u<=1j=2;endifu>1&&u<=1.4j=3;endifu>1.4j=4;endfork=i:i+2num=1;fora=i:i+2ifa~=knum=num*(t-0.2*(a-1))/(0.2*(k-1)-0.2*(a-1));endendl(k)=num;endforr=j:j+2num=1;fora=j:j+2ifa~=rnum=num*(u-0.4*(a-1))/(0.4*(r-1)-0.4*(a-1));endendm(r)=num;endsum=0;fork=i:i+2forr=j:j+2sum=sum+l(k)*m(r)*z(k,r);endendf=sum;最小二乘曲面擬合子程序：function[C,k,sigma]=fitxy(A)k=1;N=10;whilek<NB=ones(11,k+1);G=ones(21,k+1);fori=1:kforl=1:11B(l,i+1)=(0.08*(l-1)1i;endform=1:21G(m,i+1)=(0.5+0.05*(m-1))Ai;endendU=zeros(11,21);fori=1:11forj=1:21U(i,j)=A((i-1)*21+j,3);endendC=(B'*B)A-1*B'*U*G*(G'*G)A-1;sigma=0;fori=1:11forj=1:21p=0;forr=0:kfors=0:kp=p+C(r+1,s+1)*(0.08*(i-1))Ar*(0.5+(0.05*(j-1)))As;endendsigma=sigma+(U(i,j)-p)人2;endEndksigmaifsigma<=1e-7break;endk=k+1;end主程序：clc;clear;A1=zeros(11*21,3);fori=1:11x(i)=0.08*(i-1);forj=1:21y(j)=0.5+0.05*(j-1);[t(i,j),u(i,j)]=newt(x(i),y(j));A1((i-1)*21+j,1)=x(i);A1((i-1)*21+j,2)=y(j);A1((i-1)*21+j,3)=p22(t(i,j),u(i,j));endend[C,k,sigma]=fitxy(A1);A2=zeros(40,4);fori=1:8x1(i)=0.1*i;forj=1:5y1(j)=0.5+0.2*j;[t1(i,j),u1(i,j)]=newt(x1(i),y1(j));A2((i-1)*5+j,1)=x1(i);A2((i-1)*5+j,2)=y1(j);A2((i-1)*5+j,3)=p22(t1(i,j),u1(i,j));endendfori=1:8forj=1:5p=0;forr=0:kfors=0:kp=p+C(r+1,s+1)*(0.1*iJr*(0.5+(0.2*j)1s;endendA2((i-1)*5+j,4)=p;endendA1A2程序結(jié)果：數(shù)表：(x,y,f(x,y))iiiilj■jijljIj■jijljIj■jijljIj■jij■jIj■jij■jIj'j.0800000000000C"jij.0800000000000000.0800000000000000.080000000000000'j.0800000000000C"jij.0800000000000000.0800000000000000.0800000000000000.000000000000000ij.080000000000000o.aaooooooaaaMoo0.0800000000000000.OOOOOOOOOQOOOOOij.080000000000000o.aaooooooaaaMoo0.0800000000000000.OOOOOOOOOQOOOOOij.080000000000000o.aaooooooaaaMoo0.0800000000000000.080000000000000a.500000000000000a.650000000000000a.600000000000000lj.65ijLiLiLiLiLlOuij0CiLiLia.700000000000000a.750000000000000a.800000000000000lj.SSijLiLiLiijilOuijOCiLiLia.900000000000000a.950000000000000i.ooooooaoooooooa1.uSijLiLiLiijilOuijOCiLiLii.loooooooooooooa1.1500000000000001.2000000000000001.2500000000000001.3000000000000001.35'jOOOOOOC"JOOOO1.4000000000000001.4500000000000001.5000000000000000.50'jOOOOOOC"JOOOOa.5500000000000000.600000000000000a.6500000000000000.TO'jOOOOOOC'COOOOa.7500000000000000.800000000000000a.850000000000000a.900000000000000a.950000000000000i.ooooaQaofloocnoa1.050000000000003i.loooooooooocnoa1.150000000000003i.20ooaaa（M）oocnoa1.250000000000000i.soooooooooocnoa1.350000000000000i.40ooaaa（M）oocnoa1.4500000000000001.5000000000000000.446504018479934■j.32468326292743C0.2L01596S66825490.1030436083159470.003401895502659-j.08873581363800^-0.173371633749730-0.2505346114S6609-0.320276506387631-j.382668066109709-0.437795766738356-0.485758941443773TL525M7254883328-j.66063847979651C-0.587796538767667-0.60S269779089934-0.622189452876368-0.629688378L856C"j-0.630899760032776-0.6259561525^5434-0.6149885^66093580.6380152265102140.506611755U62U0.3821763592772150.2648634911536150.15478020028481fi0.051992683^30928-0.0434680^0204903-0.131601056788528-<'.212431008338821-0.286004551058031-0.352386078979359-0.411655456522184-j.463904911518766-0.50923672^700547-0.547761U796233C-0.579594388339078-j.604857258889532-0.623673421331758-0.63616824841325B-0.642467656690050-j.64369710369961C0.1,600000000000000.160000000000000ij.L.6(MOOOOOa(WOOD0.L600000000000000.LfiMOOOOOOCKOOC0.1600000000000000.16MMMOTMMM0.L600000000000000.LSOOOCOOC'OOOOO'j0.1600000000000000.LfiODOOOOOQCNOOO0.L600000000000000.1,600000000000000.1600000000000000.L600000000000000.L600000000000000.LfiMNOOtMDMMMNO0.1600000000000000.L600000000000000.1.6M)0OOOOO(W00O0.LfiMNOOtMDMMMNO0.24MQ口OO口口制QQU0.2400000000000000.2400000000000000.2400000000000000.2400000000000000.2400000000000000.2400000000000000.2400000000000000.2441OOOOOOQCN0000.2400000000000000.aWMQQOOQQ制口QQ0.2400000000000000.2400000000000000.2400000000000000.2400000000000000.2400000000000000.2400000000000000.2400000000000000.2400000000000000.2441OOOOOOOM)0000.240000000000000a.bCiuijOOuCiuuCiCiuOua.550000000000000a.64NoooaaooooM)aa.650000000000000a.74H1CCM)OCH)OOOM)0a.7500000000000000.800000000000000a.8500000000000000.900COOOOOOOOOOOa.950000000000000i.o?uoc)OQaooooM)a1.050000000000000i.looooooaooooooo1.1500000000000001.2000000300000001.2500000000000001.3000000300000001.3500000000000001.4000000300000001.dSflOOO口CMM)口MO1.500000030000000a.soo-jLiouLiooOijoooa.5500000000000000.600000000000000a.6500000000000000.700000000000000a.7500000000000000.300000000000000a.850000000000000O.900DCM)QaOOQOCNOa.950000000000000i.o?uoc)OQaooooM)a1.050000030000000i.looooooaooooooo1.1500000300000001.2000000300000001.2500000000000001.300000030000000i.354DooacN)ooooea1.4000000300000001.4EOOOOOaOOOOOCO1.5000000300000000.8400813957651430.6997S4165fi725700.56604391716081175210.3192421380407500.2063761923873720.10063S523S9H30O.LIO2O0O74OO67835-0,C893540247669S1-0851-0.2507939561598S1-0.320932269444612-u.384O37735'jD4504-0.440382175417512-0.4B9881152312579-4L532697S65S33795-0.568941879292127-0.598726549515135-0.6221S8629750329-0.639386535^97154-0.6504333507878421.LI51515091S012530.9029274308303200.7605S02663592530.6247151981d54820.495513756000S520.3731340427745030.2576567483723i10.149150559410229U.il4764S9867733S6-0.046849323201452-0.134355760504909-0.21^913344927402-0.288573700634809-0.355406364785714-0.4154913964BB576-0.468918249969472-0.515783883124747-O.E56191075200144-0.59034S930562859-U.6180S1548241234-0.6397468392578560.3200000000000000.3201)000000000000.3200000000000000.3200000000000000.3200000000000000.3200000000000000.3200000000000000.3200000000000000.32m000口MM口口00.320000000000000U.aaoouijooLiJoouuij0.3200000000000000.3200000000000000.3200000000000000.3200000000000000.3200000000000000.320口QQOOQ口口口口口Q0.3200000000000000.3201)000000000000.3200000000000000.3200000000000000.4000000000000000.400000000000000ij.4000000000000000.4000000000000000.4000000000000000.4000000000000000.4000000000000000.4000000000000000.4000000000000000.4000000000000000.lOMOOOOOMNOOO0.4000000000000000.KNNOOCMJOMNOOO0.4000000000000000.4000000000000000.4000000000000000.4000000000000000.4000000000000000.4000000000000000.44)00000000000000.400000000000000a.5000000000000000.55QDOQQ0口QQQOOQa.6000000000000000.fifiODOQQaOOOOOOQa.700000000000000a.750000000000000a.800000000000000a.850000000000000a.goijoouuiioooijooua.9500000000000001.0400000CNKM10CKO1.0500000300000001.100000000000000i.i5ijooooaooooooci1.2000000000000001.25ij0000a000i300u1.3000000000000001.3500000000000001.440DOQQCNOOOCnQ1.4500000000000001.500000030000000a.500000030000000a.550000000000000a.600000090000000a.650000000000000a.Yfloooooaoooooooa.7500000000000000.300000000000000a.85ijooooaoooooou0.900000000000000a.95ijooooaooooooci1.UO'JOOJULIOiKujQCiij1.0500000300000001.1口匹OQQOQQQQQOQ1.1500000300000001.2000000000000001.2500000000000001.3000000000000001.3500000000000001.4000000000000001.4500000000000001.5000000000000001.2712467514811471.115U5201B1453790.96^607727215350u.B2034736S4743390.6824476781794030.5510852085974750.42639238590L7680.3084029956331890.1973571296919240.093105620859405-0.004285992234034-0.09^833925296887-0.17m57299。363gg3-0.255553779054632-0.325S40150157500-0.359506983363433-U.446638204599494-0.497324951767698-0.541654032699410-0.679756479795118-0.6117062801475781.498321052480S791.3349986320657361.1771251237388651.0250240550193760.8789500231743030.7391451087034730.6057i48714870910.4788838610665610.35S6506258S1S300.2451022361964270.1382S835C9284660.038154865406993-0.055252021168143-0.141986880813721-0.222094439095899-0.296635232469797-0.362679511502827-0.423306164223960-0.477601036132450-u.62665542^667202-0.5675G4743655107O.dSOOOOOOOWOOOO0.480000000000000u.48LiijuOuijiJOCiLiiJOu0.480000000000000O.dSOOOOOOOWOOOO0.4800000000000000.4300000000000000.4800000000000004.dSOWMOMOMM0.4800000000000000.4fl0MNN0MN0M?0.4800000000000000.4SQOOOOOMM]QaOO0.480000000000000348QQQ口DQQQQQQQ口0.4800000000000000.4800000000000000.4800000000000000.4800000000000000.4800000000000000.480000000000000口.56口MMQ口OW)口制口0.560000000000000u.56000OuijOOCiuJOu0.560000000000000口.56口MMQ口OW)口制口0.5600000000000000.5600000000000000.5600000000000000.5600000000000000.5600000000000000.560MMH10MNOWN0.560000000000000Q?5fiQ口口口QQOOOQCMQ0.560000000000000358QQQ口DQQQQQQQ口0.5600000000000000.5600000000000000.5600000000000000.5600000000000000.5600000000000000.5600000000000000.5000000000000000.5500000000000000.SOuOOijOCiLijuuuuij0.6500000000000000.7000000009000000.7500000000000000.3000000000000000.8500000000000000.90000c0000000t"j0.9500000000000001.0OMN0CM0MNNN01.0500000000000001.1,000000000000001.150000000000000i.zoooDoooaaooooo1.2500000000000001.3000000000000001.3500000000000001.4000000000000001.4500000000000001.500000000000000o.saoijo-jooujoooijij0.550000000000000o.植aflMoao口制時口口0.6500000000000000.7aOiJO-jOOuJOOOijij0.7500000000000000.8000000000000000.8500000000000000.9000000000000000.9500000000000001.OOMNOCMOMNNNO1.0500000000000001.1,000000000000001.150000000000000i.zoooDoooaaooooo1.250000000000000i.aaoooooooaooooo1.3500000000000001.4000000000000001.450000000000000i.saoooooooaooooo1.7315927403819381.56203^5772081081.3972169182079581.2378010067393121.LI840876326776880.9363227723148660.7947044490537020.6593871980282330.5304S75368399490.4080886854542330.2922442012255410.182982206853550瓦LI80508434035426-0.0157904130516^1-0.1053445516209V8-0.188398090609593-0.265007L4931B92L-0.335237S38904026-0.399164503886759-0.456S68U3301565-0.50843499327B1881.97122178639SS881.7953295395006641.624067L132279061.4578305827077631.2969546497521151.1417181054472230.9923相5333M3220.8490326633293850.7119113522641070.5810941589218540.45e6585132334500.338654496139362LL22710825576S6300.122025089193158CL023392219637604-0.0685187019710a1-0.1546493i4212873-0.234152666458688-0.3073910919132B8-0.374434862348062-0.4353605565358830.560000000000000D.644MNOOCKQ(MNOO0.640000000000000■j.64000U'jOOuaoOuij0.640000000000000D.644MNOOCKQ(MNOO0.6400000000000000.6400000000000000.640000000000000ij.6400000000000000.6400000000000000.640000000000000■j.￡40000000000000ij.6400000000000001j.640uuuijCiLiLiLiOOuij0.640000000000000■j.￡40000000000000ij.640000000000000■j.64O000'j'JC"jO00C"j0.640000000000000■j.6400000000000C"j0.6400000000000000.7200000000000000.720000000000000■j.7200000000000000.720000000000000o.720oooooaaa(Noo0.7200000000000000.7200000000000000.720000000000000o.720oooooaaa(Noo0.7200000000000000.7200000000000000.7200000000000000.7200000000000000.7200000000000000.7200000000000001j.72000ijijOCiuiJOOijij0.7200000000000001j.72000uijOCiuOO0uij0.7200000000000001j.72000ijijOCiuiJOOijij0.7200000000000001.5000000000000000.50DOOQQMNOOCnoaa.550000000000000a.fiooooooMNOocnoaa.650000000000000a.ToooooQMNOocnoaa.750000000000000a.800000000000000a.850000000000000a.900000000000000a.950000000000000i.ooooooooooooooa1.050000000000000i.loijoooaoooooooa1.15ijLiLiLiLiLlOuij0CiLiLi1.2000000000000001.2SOOOOOOOOOOOOO1.3000000000000001.35Q0口心QQQQMM1.4000000000000001.45'jOOOOOOC"JOOOO1.5000000000000000.500000000000000a.550000000000000a.fioooooooooocHaaa.650000000000000a.ToocaaaoDoocnoaa.750000000000000a.soooooooooocnoaa.850000000000000a.90ooaaa(M)oocnoaa.950000000000000i.ooooooooooooooa1.050000000000003i.loooooaoooooooa1.1500000000000001.2000000000000001.250000004000000i.aoijoooaoooooooa1.3&OOOOOKWOOOOOO1.iOijOOOOOOOQOOOa1.國DO口OKM0口OC州1.500000000000000-0.4353605565358832.2156678656876742.0342011336072231.8569551436190361.6843581641610151.5167763523399551.3545190411513991.1978440866726771.0469630494193960.9020460838022630.7632264776628710.630604821954330■j.6042528146372240.5842167155456661j.270520476640969Ol163168572399612■j.06214856811676C-0.032566619396817-fl.121016534844362-0.203251399622820-0.27333035955842fi-0.5433199575400052.4646842226595632.2780589793985342.09525125084029C1.9167181279372891.7428546287758791.5739984273341241.4ia43485523083C1.2524017506080481.lC"?a944096279670.9536698512612720.8132510552488830.6789307429659430.5507748485043260.42882567697307E0.3131047717398161j.2036155U032693Ol10034547S2408951j.003268565186572-0.087653065913286-fl.172467247818847-0.2512302207523340.8000000000000000.SaOO'j'jOOj'JOOuu-j0.8000000000000000.普口QQQQQQQQQOQQQ0.8000000000000000.SINNOOCMJOMN0000.8000000000000000.8000000000000000.8000000000000000.8000000000000000.8000000000000000.8000000000000000.8000000000000000.800000000000000ij.SOOOuijOCiLiLiuuuuij0.8000000000000000.9000000000000000.8000000000000000.SOOOuijOCiLiLiuuuuij0.8000000000000000.900000000000000a.5000000300000000.55'jOOuiOQOQ'jDOua.6000000300000000.fifiGOOOOMNMlOCnOa.7000000300000000.75'jOOuiOQOQ'jDOua.800000030000000a.850000000000000a.soooooaaoooooooa.950000000000000i.ooooooaaooooooo1.050000000000000i.loooooaaooooooo1.1500003000000001.3000000000000001.2500000000000001.3000000000000001.3500000000000001.4400000000000001.450000000000000l.SOODOOOMOOOOOOO2.7178111094685702.5263395012557312.338411386B597642.1543293772803301.9745745566520321.7995105790994S71.6294482205540511.4646500437506481.3063349676606761.1516826213069641.00383741S9055120.8619123372279250.7269323711111690.5961377115200850.4723866279135940.35^758095897906u.2432541841812970.1578S22225347210.038556770326403-0-054693595934i58-u.141949659708795sigma=3.220908973633422sigma=0.iJLia659960033246式gma=1.721L7537930a078e-004sigma-3.30953430ij965474e-ijCl6k=5sigma=2.5il3781U3038OCe-OO8數(shù)表(X*,y*,/(X*,y*),Mx*，y*))：

ijijijo.laooooooaoooooa■j.100000000000000o.laooooooaoooooa0.14MOOOOOWNOOOOo.laooooooaoooooa0.2000000000000000.200000000000000Ij.200000000000000C'.SOOOOOOOOOOCOOOij.aaooooooaoooooa0.3000000000000000.3000000000000000.300000000000000ij.3000000000000000.3000000000000000.44MDMM)0(??000ao.aaooooooaoooooa0.400000000000000u.laooooooaoooooao.44Momoooooooo0.500000000000000o.baooooooaoooooa0.5000000000000000.5000000000000000.500000000000000o.eaooooooaoooooaO.fitMOOOOOWNOOOOo.eaooooooaoooooao.eaooooooaoooooao.Baooooooaoooooa0.700000000000000O.YOOOOCXIOaOOOOQOij.vaooooooaoooooa0.700000000000000o.vaooooooaoooooa0.800000000000000o.saooooooaoooooao.saooooooaoooooaO.SMOMKOMraOOOao.saooooooaoooooa0.7000000000000000.900000000000000i.looooooaoooooao1.34NNOOOCWOOO(MW1.5000000000000000.700000000000000a.91N0OOQCN0OCM)O0i.looooo