北航數(shù)值分析第三次大作業(yè)

1、北航數(shù)值分析第三次大作業(yè)數(shù)值分析第三次大作業(yè)一、算法的設(shè)計方案：（一）、總體方案設(shè)計:（1）解非線性方程組。將給定的（“，,）當作 已知量代入題目給定的非線性方程組，求得與 （2,）相對應(yīng)的數(shù)組 t i j, ui j o（2）分片二次代數(shù)插值。通過分片二次代數(shù)插值運算，得到與數(shù)組till 21,ull 21 對應(yīng)的數(shù)組z 11 21,得到二元函數(shù)z-,） o（3）曲面擬合。利用 xi,yj,zll 21建立二維函數(shù)表，再根據(jù)精度的要求選擇適當k值，并得到曲面擬合的系數(shù)矩陣Crs。(4)觀察和p(x,y)的逼近效果。觀察逼近效果只需要重復(fù)上面（1）和（2）的過程，得到與新的插值節(jié)點即,）對應(yīng)的

2、/Uo;）， 再與對應(yīng)的 P。，）：）比較即可，這里求解（，）；） 的 Cr s和 ko可以直接使用（3）中（二）具體算法設(shè)計：（1）解非線性方程組牛頓法解方程組“0 =。的解，可采用如下算 法：1）在，附近選取X*%給定精度水平£。和 最大迭代次數(shù)Mo2）對于%=0,1, M執(zhí)行計算尸淖）和尸（X）。求解關(guān)于的線性方程組尸'（a"）=-f（?。┤?"/網(wǎng)L%，則取心一，并停止計算;否則轉(zhuǎn)。計算 小川=/W。若女，則繼續(xù)，否則，輸出M次迭代不成功的信息，并停止計算。（2）分片雙二次插值給定已知數(shù)表以及需要插值的節(jié)點，進行分片二次插值的算法:設(shè)已知數(shù)表中的點

3、為： ，需要插值的節(jié)點為（小。1）根據(jù)（2）選擇插值節(jié)點 （x,，X）:插值節(jié)點對應(yīng)插值節(jié)點對i = 1 或 i = 一 1，若/»+;或應(yīng)取j = 1或/ = m-l oxi-<x<xi+2<i <n-2 匕一：<)'«力+5,24/<機_2則選擇 (積% )(%=+1;，= /-1J/+1) 為插值節(jié)點。2）計算r - r4（X）= n （女=i T" +1） 亡占4 - %v - vy） = n-=+/./-I Jr - y /xr插值多項式的公式為：p（x，y）=£ 自/式（七）氏-j-l r-j-l注

4、:本步進行插值運算的是&"）,利用因力） 與a”）的對應(yīng)關(guān)系就可以得到;與（專匕）的對應(yīng) 關(guān)系。（3）曲面擬合根據(jù)插值得到的數(shù)表進行曲面擬合的過程：1）根據(jù)擬合節(jié)點和基底函數(shù)寫出矩陣B 和G：J（力（X）l （X）"1（“。（y。）"（y°y （兒，、 （y）° （力（）j1（%）'-%）2）計算 C =3 B）7 B/UG©G）T O在這里，為了簡化計算和編程、避免矩陣 求逆，記：A = （4 8尸 BtU , Dt = G（GG尸對上面兩式進行變形，得到如下兩個線性方程組：= BtU , （G，G）D = Gt通過

5、解上述兩個線性方程組，則有：C = ADT3）對于每一個 （,“）,P（X” X）= Z Z J （“' （.）' Or=0 $=04）擬合需要達到的精度條件為：n inb = Z方p（%，X）一%。r-0 ”其中.對應(yīng)著插值得到的數(shù)表知力,/（冷X）中/X）的值。5）讓k逐步增加，每一次重復(fù)執(zhí)行以上幾步，直到b=-p'a，x）1。-7 成立。此時的k1-（） ;-0值就是要求解最小的鼠二、源程序:#include<stdioe h>#include<iostream>#include<stdlib. h>#include<ma

6、th. h>#include<float. h>#include<iomanip>ttdefine Epsilonl le-12/*解線性方程組時近似解向量的精度*/ttdefine M 200/*解線性方程組時的最大迭代次數(shù)*/ftdefine N 10/*求解迭代次數(shù)時假設(shè)的k的最大值,用于定義包含k的存儲空間*/void Newton () ;/*牛頓法求解非線性方程組子程序*/void fpeccz () ;/*分片二次代數(shù)插值子程序*/void qmnh () ;/*曲面擬合子程序*/void duibi () ;/*對比/和p逼近效果的子doublex

7、ll,y21,tll 21,ull 21;/* 定義全局變量*/double zll 21,C10 10;double kz;void Newton (double xll, double y21)/* 牛頓法求解非線性方程組子程序*/(doubleX 4, dx 4, F4, dF 4 4, temp, m, fx, fX;int i, j,k, l,p, ik,n;for(i=0;i<=10;i+)(for(j=0;j<=20;j+)(X0=l;/*選取迭代初始向量,四個分別代表t, u, V, W*/X =1;X3=l;n=0;loopl: F0 =0. 5*cos(X0)+

8、Xl +X2 +X3-xi-2. 67;F1=XO+O. 5*sin(Xl)+X2+X3-yj- L07;F2 =0. 5*X0 +X1 +cos(X2)+X3-xi- 3. 74;F3=X0 +0. 5*X1 +X2 +sin(X)-yj- 0. 79;/*求解 F (x) */dF0 0=-0. 5*sin(X0); /*求解 F'(x) */dF0l=l;dF0 2=1;dF0 3=1;dFl0=l;dFll=0. 5*cos(Xl);dFl2=l;dFl3=l; dF2 0=0.5;dF2l=l;dF2 2=-sin(X2);dF2 3=1;dF3 0=l;dF3l=0.5;d

9、F3 2=1;dF3 3=cos(X3);/*高斯選主元消去法求解A x*/ for(k=0;k<3;k+) ik=k;for(l=k;1<=3;1+)if(dFik k<dFl k) ik=l; /*選主元*/temp=0; temp=Fik; Fik=Fk; Fk=temp;for(l=k;1<=3;1+) temp=0;temp=dFik1;dFEik l=dFk 1;dFk l=temp;)for (l=k+l;1<=3;1+)(m=dFl k/dFk k;Fl=Fl-m*Fk;for(p=k+l;p<=3;p+)dFl p=dFl p-m*dFk

10、p; /*消去過程*/dx3=-F3/dF3 3;for(k=2;k>=0;k一)temp=0;for(l=k+l;1<=3;1+)temp=temp+dFkl*dxl/dFkk;dxk=-Fk/dFkk-temp;)temp=O;for(l=0;l<=3;l+)/* 求解矩陣范數(shù)，用無窮范數(shù)*/(if (temp<fabs (dx 1)temp=fabs(dx11);)fx=temp;temp=O;for(l=0;l<=3;l+)(if(temp<fabs(X1) temp=fabs(X1J);fX二temp;if (fabs(fx/fX)<Epsi

11、lonl) /* 判斷 131L/HL會是否成立*/ui j=Xl;goto loop4; else for(l=0;l<=3;l+)Xl=Xl+dXl;n=n+l;goto loop3;loop3: if (n<M)/*判斷是否超出規(guī)定迭代次數(shù)*/goto loopl;elseprintf ("迭代不成功n");goto loop4; loop4:continue; )void fpeccz (double t1121, doubleull 21)/*分片二次代數(shù)插值子程序*/(int sll 21,rll 21;int i, j, il, jl,m;doub

12、lez06 6 = -0, 5, -0. 34, 0.14, 0. 94, 2. 06, 3. 5),-0. 42, -0. 5, -0. 26, 0. 3,1.18, 2. 38),-0. 18, -0. 5, -0. 5, -0. 18, 0. 46, 1. 42,0. 22, -0. 34, -0. 58, -0. 5, -0. 1, 0. 62,0. 78, -0. 02, -0. 5, -0. 66, -0. 5, -0. 02),1. 5, 0, 46, -0. 26, -0. 66, -0. 74, -0. 5;double t06 = 0, 0. 2, 0. 4, 0. 6,

13、0, 8, 1. 0;double uO 6 = 0, 0. 4, 0. 8, L 2, 1. 6, 2. 0; double tempi, temp2;for(i=0;i<=10;i+) /* 選取插值節(jié)點*/for(j=0;j<=20;j+)(if (ti j<=0. 3)si j=l;elseif (ti j>0. 7)si j=4;else(for (m=2; m<=3; m+)if (ti j>0. 2*m-0. l)&&(t i j<=0> 2*m+0. 1)(si)for(i=0;i<=10;i+)(if (u

14、i j<=0. 6)ri j=l;elseif (ui j>l. 4)ri j=4;else(for (m=2; m<=3 ;m+)if (ui j>0. 4*m-0. 2)&&(ui j<=0. 4*m +0. 2)(ri)for(i=0;i<=10;i+)/* 插值運算*/(zi j=0;for(il=sEij+l;il+)for(jl=ri jl<=ri j+l; jl+) (templ=l. 0;for (m=si j-l;m<=si j+l;m+) if(m!=il)templ*=(ti j-t0m)/ (t0il-t0

15、m);) temp2=l. 0;for (m=ri j-l;m<=ri j+l;m+) if(m!=jl)temp2*=(ui j-u0m)/ (u0jl-u0m);)zi j +=templ*temp2*z0i 1 jl;)void qmnh ()/*曲面擬合子程序*/ int i, j, k, m, 1, il, jl, ik;doubleAN 21,DN 21,B11 N,BtN 11, BtB N N, BtU N 21, BtBl N N; doubleG21 N, Gt N 21, GtGN N, GtGl N N. Jdouble sigma, pll 21, temp,

16、q;printf ("選擇過程的k和sigma值:n");k=0;sigma=l; /*選取初值，使循環(huán)開始*/*求解系數(shù)矩陣Crs*/ while (sigma>le-7)for(i=0;i<=10;i+)for(j=0;j<=k;j+)Bi j=pow(xi, j);Btj i=Bi j;)for (i=0;i<=k;i+)(for(j=0;j<=k;j+) *temp=0;for (1=0;1<=10;1+) temp+=Bti 1*B1 j; BtBi j=temp;for(i=0;i<=k;i+)for(j=0;j<

17、=20;j+)(temp=O;for(l=0;l<=10;l+) temp+=Bti l*zl j ; BtUi j=temp;)for(1=0;l<=20;1+)(for (i=0;i<=k;i+)(for(j=0;j<=k;j+) BtBlij=BtBi j; )for(m=0;m<=k-l;m+)(ik=m;for(i=m;i<=k-l;i+)if (fabs(BtBli m) <fabs (BtBl i+1 m) ik=i+l;else ;)if (ik!=m)(for(i=m;i<=k;i+)(temp=BtBlmi;BtBlik i=

18、temp;)temp=BtU Em 1;BtUm l=BtUikl; BtUik l=temp;for(i=m+l;i<=k;i+)q=BtBlim/BtBlmm;for(j=m;j<=k;j+) BtBlEi j=BtBlij; BtUi l=BtUi l-q*BtUm 1;)Ak l=BtUk l/BtBlk k;for (m=k-l; m>=0; m一)(temp=0;for (i=m+l;i<=k;i+) temp+=Aii; Aml-temp)/BtBl m m;)for (i=0;i<=20;i+)for(j=0;j<=k;j+)Gi jzzpo

19、w(yi, j);Gtji=Gi j;)for(i=0;i<=k;i+)( for(j=0;j<=k;j+)(temp=O;for(m=0;m<=20;m+) temp+=GtEij; GtGi j=temp;for(1=0;l<=20;1+)for(i=0;i<=k;i+) for(j=0;j<=k;j+) GtGlij=GtGij; for (m=0; m<=k-l; m+)(ik=m;for(i=m;i<=k-l;i+)(if(fabs(GtGlim)<fabs(GtGli+1m) ik=i+l;else ;if (ik!=m)(fo

20、r (i=m; i<=k; i+)(temp=GtGlmi;GtGlEm i=GtGliki;GtGlik i=temp;temp二Gt m 1;Gtm l=Gtik 1;Gt ik l=temp;for(i=m+l;i<=k;i+)(q=GtGlim/GtGlmm;for(j=m;j<=k;j+) GtGlij=GtGlij-q*GtGlmj; Gti l=Gti1;)Dk l=Gtk l/GtGlk k;for (m=k-l; m>=0; m)temp=0;for (i=m+l;i<=k;i+) temp+=Di l*GtGlm i; Dm l =(Gt m

21、1-temp)/GtGl m m; )for(i=0;i<=k;i+)(for(j=0;j<=k;j+)(temp=O;for (m=0;m<=20;m+) temp+=Aim; Ci j=temp;)sigma=0;/*歸零，開始計算sigma值*/ for(i=0;i<=10;i+) for(j=0;j<=20;j+)(pi j=0;for (il=O;il<=k;il+) for (j1=0;jl<=k;j1+) pi jl+=Cil jl*pow(xi, il)*pow(y ULji); sigma+=pow(pi j-zi j, 2); )p

22、rintf("k=%dsigma=%. 12enz，, k, sigma);k=k+l; printf ("達到精度要求時的k和sigma值:n");printf("k=%dsigma=%. 12en”, k, sigma);kz=k; /*定義為全局變量，便于duibi ()調(diào)用*/)void duibi () /*對比/和p逼近效果的子程 序*/ int i, j, il, jl;double p85;for(i=0;i<=7;i+)(for(j=0;j<=4;j+)(xi=0. l*(i+l);yj=O. 5+0. 2*(j+l); /

23、*重新輸入節(jié) 點*/Newton (x, y);fpeccz (t, u);/*求解f (x*, y*) */for(i=0;i<=7;i+) /*求解 p (x y*) */for(j=0;j<=4;j+)pi j=0;for (il=O; iK=kz; il+)for (j1=0;jl<=kz;j1+) pi j+=Cil jl*pow(xi, il)*pow(y)printf (“x %d =%. 6f y%d =%. 6fn”, i+1, xi, j+1, yjl);printf (f (x %d, y %d) =%. 12en, i+1, j+1printf (p

24、(x %d, y %d) =%. 12en, i+1, j+1 ,pi j);printf C。=%. 12en, zij); /*數(shù)表 y4/ (xj, y；),p(Xi*, yA) */ void main () int i, j;for(i=0;i<=10;i+)for(j=0;j<=20;j+)(xi=0. 08*i;y j =0. 5+0. 05*j; /*輸入節(jié)點*/ Newton (x, y);fpeccz (t, u);for(i=0;i<=10;i+)(for(j=0;j<=20;j+)(printf ("x %d =%. 6f y %d =

25、%. 6f zE%d %d=%. 12en”, i, xi, j, yj, i, j, zi j); /*數(shù)表：Xi, yo f(X1, yt)*/qmnh ();for(i=0;i<=kz;i+)for(j=0;j<=kz;j+)printf CC%d %d=%. 12en”, i, j, Ci j);/*數(shù)表:Cr s*/duibi ();)三、運行結(jié)果輸出1、數(shù)表數(shù)表： Xi, Yi,/ (Xi, yjz00=4. 465040184807e-001z0l=3. 246832629277e-001x0=0. 000000x0=0. 000000y0=0. 500000yl=0

26、. 550000z03=1. 030436083160e-001z04=3. 401895562675e-003z05=-8. 873581363800e-002z06=-l. 733716327497e-001z07=-2. 505346114666e-001z08=-3. 202765063876e-001z09=-3. 826680661097e-001z010=-4. 377957667384e-001z0ll=-4. 857589414438e-001 z012=-5. 266672548835e-001 z013=-5. 606384797965e-001 z014=-5. 877

27、965387677e-001 z015=-6. 082697790899e-001 z016=-6. 221894528764e-001 z017=-6. 296883781856e-001 z018=-6. 308997600028e-001 z019=-6.259561525454e-001x0=0.000000x0=0. 000000x0=0.000000x0=0.000000x0=0.000000x0=0. 000000x0=0. 000000x0=0.000000x0=0. 000000x0=0.000000x0=0.000000x0=0. 000000x0=0.000000x0=0

28、. 000000x0=0.000000x0=0.000000x0=0. 000000y3=0. 650000 y4=0. 700000 y5=0. 750000 y6=0. 800000 y7=0. 850000 y8=0. 900000 y9=0. 950000 y 10 =1.000000 yU=l. 050000 y12=l. 100000 y13=l. 150000 y 14 =1.200000 y15=l. 250000 y16=l. 300000 y17=l. 350000 y 18=1.400000 y19=l. 450000zl0=6. 380152265113e-001 zl

29、l=5. 066117551467e-001 zl2=3. 821763692774e-001 zl3=2. 648634911537e-001 zl4=l. 547802002848e-001xl=0. 080000xl=0. 080000xl=0.080000xl=0. 080000xl=0.080000y0=0. 500000yl=0. 550000y2=0. 600000y3=0. 650000y4=0. 700000xl=0.080000y6=0. 800000zl6=-4. 346804020490e-002zl9=-2. 860045510580e-001zl10=-3. 523

30、860789794e-001xl=0. 080000xl=0.080000y9=0. 950000y 10 =1.000000zl12=-4. 639049115188e-001 zl13=-5. 092367247005e-001 zl14=-5. 47761 U79623e-001 zl15=-5. 795943883391e-001 zl16=-6.048572588895e-001 zl17=-6. 236734213318e-001 zl18=-6. 361682484133e-001 zl19=-6. 424676566901e-001 zl20=-6. 426971026996e

31、-001 z20=8. 400813957666e-001 z2l=6. 997641656732e-001 z22=5. 660614423517e-001 z2 3 =4. 39171608U76e-001z2 5=2.063761923874e-001 z26=1. 006385238914e-001 z27=2. 060740067837e-003 z28=-8. 935402476698e-002 z29=-L 736269688648e-001z210=-2. 507999561599e-001 z2ll=-3. 209322694446e-001 z212=-3. 8409773

32、50046e-001 z213=-4. 403821754175e-001 z214=-4. 8988U523126e-001 z215=-5. 326979655338e-001 z216=-5. 689418792921e-001 z217=-5. 987265495151e-001 z218=-6. 221686297503e-001 z219=-6. 393865356972e-001 z220=-6. 504993507878e-001z30=l. 051515091803e+000 z3l=9. 029274308310e-001 z32=7. 605802668596e-001

33、z33=6. 247151981456e-001 z34=4. 955197560009e-001 z35=3. 731340427746e-001 z36=2. 576567488723e-001xl=0. 080000 xl=0.080000xl=0. 080000 xl=0. 080000 xl=0. 080000xl=0. 080000 xl=0. 080000 xl=0. 080000 xl=0.080000 x2=0.160000 x2=0.160000 x2=0.160000 x2=0.160000 x2=0.160000x2=0.160000x2=0.160000x2=0.16

34、0000x2=0.160000x2=0.160000x2=0.160000x2=0.160000x2=0. 160000x2=0.160000x2=0.160000x2=0.160000x2=0.160000x2=0.160000x2=0.160000x2=0.160000x3=0. 240000x3=0. 240000x3=0. 240000x3=0.240000x3=0. 240000x3=0. 240000x3=0.240000 y12=l.100000 y13=l. 150000 y 14 =1.200000 y15=l. 250000 y 16 =1.300000 y17=l. 35

35、0000 y 181=1.400000 y 191=1.450000 y 20 =1.500000 y0=0. 500000 yl=0. 550000 y2=0. 600000y3=0. 650000 y5=0. 750000 y6=0. 800000 y7=0. 850000 y8=0. 900000 y9=0. 950000 y10=l. 000000 yll=l. 050000 y12=l. 100000 y13=l. 150000 y 14 =1.200000 y15=l. 250000 y16=l. 300000 y17=L 350000 y 18 =1.400000 y19=l.

36、450000 y 20=1.500000 y0=0. 500000 yl=0. 550000 y2=0. 600000 y3=0. 650000 y4=0. 700000 y5=0. 750000 y6=0. 800000z37=1. 491505594102e-001z38=4.764698677337e-002z39=-4. 684932320146e-002z310=-l. 343567603849e-001z312=-2. 885737006348e-001z313=-3. 554063647857e-001y15=l. 250000z315=-4. 689182499695e-001

37、z317=-5. 561910752001e-001z318=-5. 902469305629e-001z320=-6. 397468392579e-001 z40=l. 271246751483e+000z42=9. 646077272157e-001z43=8. 203473694751e-001z44=6. 824476781795e-001z46=4. 263923859018e-001z47=3. 084629956332e-001z48=1. 973571296919e-001z410=-4. 285992234033e-003 z4ll=-9. 483392529689e-002

38、 z412=-1. 785729903640e-001 z413=-2. 555537790546e-001 z414=-3. 258401501575e-001 z415=-3. 895069883634e-001 z416=-4. 466382045995e-001 z417=-4. 973249517677e-001y19=l. 450000z419=-5. 797564797951e-001z50=l.498321052482e+000z5l=l. 334998632066e+000z53=L 025024055020e+000 z5 4=8. 789600231744e-001 z5

39、5=7. 391451087035e-001 z56=6. 057448714871e-001 z57=4. 788838610666e-001 z58=3. 586506258818e-001x3=0. 240000 x3=0. 240000 x3=0. 240000 x3=0. 240000x3=0. 240000 x3=0. 240000x3=0. 240000x3=0. 240000 x3=0. 240000x3=0. 240000 x4=0. 320000x4=0. 320000 x4=0. 320000 x4=0. 320000x4=0. 320000 x4=0. 320000 x

40、4=0. 320000x4=0. 320000 x4=0. 320000 x4=0. 320000 x4=0. 320000 x4=0. 320000 x4=0. 320000 x4=0. 320000 x4=0. 320000x4=0. 320000x5=0.400000 x5=0.400000x5=0.400000 x =0.400000 x5=0. 400000 x5=0.400000 x5=0. 400000 x =0.400000y7=0. 850000y8=0. 900000y9=0. 950000 y 10 =1.000000 y12=l. 100000y13=l. 150000

41、 y17=l. 350000 y 181=1.400000 y 20 =1.500000 y0=0. 500000 y2=0. 600000y3=0. 650000y4=0. 700000 y6=0. 800000y7=0. 850000y8=0. 900000 y 10 =1.000000 yll=l. 050000 y12=L 100000 y13=l. 150000 y 14 =1.200000 y15=l. 250000 y16=l. 300000 y17=l. 350000 y0=0. 500000yl=0. 550000 y3=0. 650000y4=0. 700000y5=0.

42、750000y6=0. 800000y7=0. 850000y8=0. 900000z59=2. 451022361964e-001z510=l. 382683509285e-001x5=0.400000x5=0.400000y9=0. 950000y10=l. 000000x5=0.400000y12=l. 100000z512=-5. 525282116814e-002z514=-2. 220944390959e-001 z515=-2. 956352324598e-001 z516=-3. 626795115028e-001 z517=-4. 233061642240e-001 z518

43、=-4. 776010361325e-001 z519=-5. 256554266672e-001 z520=-5. 675647436551e-001 z60=l. 731892740383e+000 z6l=l. 562034577209e+000 z62=1. 397216918208e+000 z63=1. 237801006739e+000 z64=1. 084087532678e+000 z65=9. 363227723149e-001 z66=7. 947044490537e-001 z67=6. 593871980282e-001 z68=5. 304875868400e-00

44、1 z69=4. 080886854542e-001z610=2. 922442012295e-001 z6ll=l. 829822068536e-001 z612=8. 030849403543e-002 z613=-l. 579041305164e-002 z614=-l. 053445516210e-001 z615=-l. 883980906096e-001 z616=-2. 650071493189e-001 z617=-3. 352378389040e-001 z618=-3. 991645038868e-001 z619=-4. 568681433016e-001 z620=-5

45、. 084349932782e-001 z70=l. 971221786400e+000 z779532959950le+000 z72=1. 624067113228e+000 z73=1.457830582708e+000 z74=1. 296954649752e+000x5=0.400000x5=0.400000x5=0.400000x5=0.400000x5=0.400000x5=0. 400000x5=0.400000x6=0.480000x6=0.480000x6=0.480000x6=0. 480000x6=0.480000x6=0.480000x6=0.480000x6=0.4

46、80000x6=0.480000x6=0.480000x6=0. 480000x6=0.480000x6=0.480000x6=0.480000x6=0.480000x6=0.480000x6=0.480000x6=0.480000x6=0.480000x6=0.480000x6=0.480000x7=0.560000x7=0.560000x7=0.560000x7=0.560000x7=0. 560000y 14 =1.200000 y15=l. 250000 y16=l. 300000 y17=l. 350000 y 18 =1.400000 y 19 =1.450000 y 20 =1.

47、500000 y0=0. 500000 yl=0. 550000 y2=0. 600000 y3=0. 650000 y4=0. 700000 y5=0. 750000 y6=0. 800000 y7=0. 850000 y8=0. 900000 y9=0. 950000 y10=l. 000000 yll=l. 050000 y12=l. 100000 y13=l. 150000 y 14 =1.200000 y15=l. 250000 y 16 =1.300000 y17=l. 350000 y 18 =1.400000 y19=l. 450000 y 20 =1.500000 y0=0.

48、 500000 yl=0. 550000 y2=0. 600000 y3=0. 650000 y4=0. 700000z76=9. 923495333243e-001z7 7=8. 490326633294e-001x7=0. 560000x7=0. 560000y6=0. 800000y7=0. 850000x7=0. 560000 y10=l.000000 z710=4. 566585132334e-001z711=3. 386544961394e-001 z712=2. 271082557696e-001z7220250891932e-001 z714=2. 339221963760e-

49、002z715=-6. 881870197104e-002 z716=-1. 546493442129e-001 z717=-2. 341526664587e-001 z718=-3. 073910919133e-001 z719=-3. 744348623481e-001z720=-4. 353605565359e-001x7=0.560000 x7=0. 560000x7=0. 560000 x7=0. 560000 x7=0. 560000 x7=0. 560000 x7=0. 560000 x7=0. 560000 x7=0. 560000 x7=0.560000yll=l. 050000 y12=l.100000 y13=l. 150000 y 14=1.2