1、北航数值分析大作业（三）（看到那个收 10 个财富值的就不舒服，共享的精髓就在于免费）一、题目关于 x， y， t， u， v， w 的下列方程组0.5cost+u+v+w-x=2.67t+0.5sinu+v+w-y=1.070.5t+u+cosv+w-x=3.74t+0.5u+v+sinw-y=0.79以及关于 z， t，u 的下列二维数表z ut0 0.4 0.8 1.2 1.6 20 -0.5 -0.34 0.14 0.94 2.06 3.50.2 -0.42 -0.5 -0.26 0.3 1.18 2.380.4 -0.18 -0.5 -0.5 -0.18 0.46 1.420.6 0
2、.22 -0.34 -0.58 -0.5 -0.1 0.620.8 0.78 -0.02 -0.5 -0.66 -0.5 -0.021.0 1.5 0.46 -0.26 -0.66 -0.74 -0.5确定了一个二元函数 z=f(x，y)。1试用数值方法求出 f(x，y)在区域 D=(x,y)0x0.8,0.5y1.5 上的一个近似表达式 ,0()krsrspxycxy要求 p(x,y)一最小的 k 值达到以下的精度 102 27(,)(,)10ijijijfxy其中 xi=0.08i，y j=0.5+0.05j。2计算 f(xi*,yj*),p(xi*,yj*)(i=1,2,8;j=1,2,
3、5)的值，以观察 p(x,y)逼近f(x,y)的效果，其中 xi*=0.1i,yj*=0.5+0.2j。二、算法设计方案1.将 和 代入非线性方程0.8(,10)ii .50(,120)jyj组中，用牛顿法解出 和 ；itju2.以采取分片二次插值，选择（m，n）满足 ,232mimhttnjnu如果 或 ，则 m=1 或 4；如果 或 ，则 n=112iht4it12ju42ju或 n=4。选择 为插值节点，相应的(,)1,;,)kr rLagrange 形式的插值多项式为 A12(,)()(,)mnkrkrkrptultuft其中(k=m-1, m, m+1)1()mwkktlt(r=n-
4、1, n, n+1)A1()nrwrwylu并将 和 代入 ，便得到了数表 。itju2(,)pt ,(,)ijijxfy3.进行曲面拟和系数矩阵 ，rscC11()TTBUG其中，001100()kri kxB 001100()ksj ky(,)ijfxyUk 从 0 逐渐增大，直到 ，便得到了要求精度的系数 。71rsc三、全部源程序/在 visual Studio2010 的 c 语言环境下编译通过#include#include#include #define n 4static double xn,x_n,U1121,t1121,u1121,tt85,uu85,UU85,c99;in
5、t k;double MAX(double an)/求数组中的最大值int i;double max;max=fabs(a0);for(i=0;imax)max=fabs(ai);return(max);void DooLittle(double ann,double bn)/选主元的 DooLittle 分解法求线性方程组int i,j,k,t,i_k,mn;double unn,lnn,sn,yn;double u_x,l_u,max,temp;for(k=1;kmax)max=fabs(si-1);i_k=i;mk-1=i_k;if(i_k!=k)for(t=1;t=1;i-)u_x=0
6、;for(t=i+1;t1.6) aij=1.6;if(bij0.8) bij=0.8;for(k=0;kfabs(*(a+j*la+k) j=i;if (j!=k)for (i=0; iN; i+)temp=*(a+j*la+i);*(a+j*la+i)=*(a+k*la+i);*(a+k*la+i)=temp;temp=*(b+j*lb+i);*(b+j*lb+i)=*(b+k*lb+i);*(b+k*lb+i)=temp;if (*(a+k*la+k)=0)return 0;if (temp=*(a+k*la+k)!=1)for (i=0; iN; i+)*(a+k*la+i)/=tem
7、p;*(b+k*lb+i)/=temp;for (i=0; iN; i+)if (*(a+i*la+k)!=0) for (j=0; jN; j+)*(a+i*la+j)-=temp*(*(a+k*la+j);*(b+i*lb+j)-=temp*(*(b+k*lb+j);return 0;void solve_C()int i,j,r,s;double t12121, t22121, t32121,d99,e99;double B119, B_T911, G219, G_T921,P1121;double temp, FangCha;for(i=0;i9;i+)for(j=0;j11;j+)B
8、ji=pow(0.08*j,i);B_Tij=pow(0.08*j,i);for(j=0;j21;j+)Gji=pow(0.5+0.05*j,i);G_Tij=pow(0.5+0.05*j,i); for (k=0; k9; k+) FangCha=0;Multi(B_T0, B0, t10, 11, 9, 21, k+1, 11, k+1); Inverse(t10, c0, 21, 9, k+1);Multi(e0, c0, d0, 9, 9, 9, k+1, k+1, k+1);Multi(c0, B_T0, t10, 9, 11, 21, k+1, k+1, 11);Multi(t10
9、, U0, t20, 21, 21, 21, k+1, 11, 21);Multi(G_T0, G0, t10, 21, 9, 21, k+1, 21, k+1);Inverse(t10, c0, 21, 9, k+1);Multi(G0, c0, t30, 9, 9, 21, 21, k+1, k+1);Multi(t20, t30, c0, 21, 21, 9, k+1, 21, k+1);for(i=0;i11;i+)for(j=0;j21;j+)temp=0;for(r=0;rk+1;r+)for(s=0;sk+1;s+)temp+=crs*Bir*Gjs;Pij=temp; Fang
10、Cha+=(Uij-temp)*(Uij-temp);printf(“%s%d%s%.11e%s“,“k=“,k,“; Sigma=“,FangCa,“;n“);if(FangCha=1.0e-7)printf(“%s%d%s%.11e%s“,“达到精度要求时 : k=“,k,“; sigma=“,FangCha,“;n 系数 c(r,s)如下：n“);for(i=0;ik+1;i+)for(j=0;jk+1;j+)printf(“%s%d%s%d%s%19.11e%s“,“c(“,i,“,“,j,“)=“,cij,“; “);if(j=(k-1)/2)coutendl;coutendl;co
11、utendl;return;cout“经过 8 次拟合没有达到所需精度；“endl;return;void Check()/验证子程序 int i,j,r,s;double B89,G59,temp;Lagrange( tt0,uu0,UU0,8,5,0);for(i=0;ik+1;i+)for(j=0;j8;j+)Bji=pow(0.1*(j+1),i);for(j=0;j5;j+)Gji=pow(0.5+0.2*(j+1),i);for(i=0;i8;i+)for(j=0;j5;j+)temp=0;for(r=0;rk+1;r+)for(s=0;sk+1;s+)temp+=crs*Bir*
12、Gjs;printf(“%s%d%s%.2f%s%d%s%.2f“,“x*(“ , i+1, “)=“ , 0.1*(i+1) , “, y*(“,j+1,“)=“,0.5+0.2*(j+1);printf(“%s%19.11e%s%19.11e%s“ , “, f(x*,y*)=“,UUij,“, p(x*,y*)=“,temp,“;n“);void main() void NEWTON(double,double);void DooLittle(double *,double *);void Solve_tu();void solve_C();void Check();void Lagra
13、nge(double *t,double *u,double *U,int la,int lb,int );Solve_tu();Lagrange(t0,u0,U0,11,21,1);solve_C();Check();getchar();四、程序运行结果：1. 数表：xi, yj, f(xi, yj)x( 0)=0.00, y( 0)=0.50, 4.46504018481e-001; x( 0)=0.00, y( 1)=0.55, 3.24683262928e-001;x( 0)=0.00, y( 2)=0.60, 2.10159686683e-001; x( 0)=0.00, y( 3)
14、=0.65, 1.03043608316e-001;x( 0)=0.00, y( 4)=0.70, 3.40189556268e-003; x( 0)=0.00, y( 5)=0.75, -8.87358136380e-002;x( 0)=0.00, y( 6)=0.80, -1.73371632750e-001; x( 0)=0.00, y( 7)=0.85, -2.50534611467e-001;x( 0)=0.00, y( 8)=0.90, -3.20276506388e-001; x( 0)=0.00, y( 9)=0.95, -3.82668066110e-001;x( 0)=0.
15、00, y(10)=1.00, -4.37795766738e-001; x( 0)=0.00, y(11)=1.05, -4.85758941444e-001;x( 0)=0.00, y(12)=1.10, -5.26667254884e-001; x( 0)=0.00, y(13)=1.15, -5.60638479797e-001;x( 0)=0.00, y(14)=1.20, -5.87796538768e-001; x( 0)=0.00, y(15)=1.25, -6.08269779090e-001;x( 0)=0.00, y(16)=1.30, -6.22189452876e-0
16、01; x( 0)=0.00, y(17)=1.35, -6.29688378186e-001;x( 0)=0.00, y(18)=1.40, -6.30899760003e-001; x( 0)=0.00, y(19)=1.45, -6.25956152545e-001;x( 0)=0.00, y(20)=1.50, -6.14988546609e-001;x( 1)=0.08, y( 0)=0.50, 6.38015226511e-001; x( 1)=0.08, y( 1)=0.55, 5.06611755147e-001;x( 1)=0.08, y( 2)=0.60, 3.821763
17、69277e-001; x( 1)=0.08, y( 3)=0.65, 2.64863491154e-001;x( 1)=0.08, y( 4)=0.70, 1.54780200285e-001; x( 1)=0.08, y( 5)=0.75, 5.19926834909e-002;x( 1)=0.08, y( 6)=0.80, -4.34680402049e-002; x( 1)=0.08, y( 7)=0.85, -1.31601056789e-001;x( 1)=0.08, y( 8)=0.90, -2.12431088309e-001; x( 1)=0.08, y( 9)=0.95,
18、-2.86004551058e-001;x( 1)=0.08, y(10)=1.00, -3.52386078979e-001; x( 1)=0.08, y(11)=1.05, -4.11655456522e-001;x( 1)=0.08, y(12)=1.10, -4.63904911519e-001; x( 1)=0.08, y(13)=1.15, -5.09236724701e-001;x( 1)=0.08, y(14)=1.20, -5.47761117962e-001; x( 1)=0.08, y(15)=1.25, -5.79594388339e-001;x( 1)=0.08, y
19、(16)=1.30, -6.04857258890e-001; x( 1)=0.08, y(17)=1.35, -6.23673421332e-001;x( 1)=0.08, y(18)=1.40, -6.36168248413e-001; x( 1)=0.08, y(19)=1.45, -6.42467656690e-001;x( 1)=0.08, y(20)=1.50, -6.42697102700e-001;x( 2)=0.16, y( 0)=0.50, 8.40081395767e-001; x( 2)=0.16, y( 1)=0.55, 6.99764165673e-001;x( 2
20、)=0.16, y( 2)=0.60, 5.66061442352e-001; x( 2)=0.16, y( 3)=0.65, 4.39171608118e-001;x( 2)=0.16, y( 4)=0.70, 3.19242138041e-001; x( 2)=0.16, y( 5)=0.75, 2.06376192387e-001;x( 2)=0.16, y( 6)=0.80, 1.00638523891e-001; x( 2)=0.16, y( 7)=0.85, 2.06074006784e-003;x( 2)=0.16, y( 8)=0.90, -8.93540247670e-002
21、; x( 2)=0.16, y( 9)=0.95, -1.73626968865e-001;x( 2)=0.16, y(10)=1.00, -2.50799956160e-001; x( 2)=0.16, y(11)=1.05, -3.20932269445e-001;x( 2)=0.16, y(12)=1.10, -3.84097735005e-001; x( 2)=0.16, y(13)=1.15, -4.40382175418e-001;x( 2)=0.16, y(14)=1.20, -4.89881152313e-001; x( 2)=0.16, y(15)=1.25, -5.3269
22、7965534e-001;x( 2)=0.16, y(16)=1.30, -5.68941879292e-001; x( 2)=0.16, y(17)=1.35, -5.98726549515e-001;x( 2)=0.16, y(18)=1.40, -6.22168629750e-001; x( 2)=0.16, y(19)=1.45, -6.39386535697e-001;x( 2)=0.16, y(20)=1.50, -6.50499350788e-001;x( 3)=0.24, y( 0)=0.50, 1.05151509180e+000; x( 3)=0.24, y( 1)=0.5
23、5, 9.02927430831e-001;x( 3)=0.24, y( 2)=0.60, 7.60580266860e-001; x( 3)=0.24, y( 3)=0.65, 6.24715198146e-001;x( 3)=0.24, y( 4)=0.70, 4.95519756001e-001; x( 3)=0.24, y( 5)=0.75, 3.73134042775e-001;x( 3)=0.24, y( 6)=0.80, 2.57656748872e-001; x( 3)=0.24, y( 7)=0.85, 1.49150559410e-001;x( 3)=0.24, y( 8)
24、=0.90, 4.76469867734e-002; x( 3)=0.24, y( 9)=0.95, -4.68493232015e-002;x( 3)=0.24, y(10)=1.00, -1.34356760385e-001; x( 3)=0.24, y(11)=1.05, -2.14913344927e-001;x( 3)=0.24, y(12)=1.10, -2.88573700635e-001; x( 3)=0.24, y(13)=1.15, -3.55406364786e-001;x( 3)=0.24, y(14)=1.20, -4.15491396489e-001; x( 3)=
25、0.24, y(15)=1.25, -4.68918249969e-001;x( 3)=0.24, y(16)=1.30, -5.15783883125e-001; x( 3)=0.24, y(17)=1.35, -5.56191075200e-001;x( 3)=0.24, y(18)=1.40, -5.90246930563e-001; x( 3)=0.24, y(19)=1.45, -6.18061548241e-001;x( 3)=0.24, y(20)=1.50, -6.39746839258e-001;x( 4)=0.32, y( 0)=0.50, 1.27124675148e+0
26、00; x( 4)=0.32, y( 1)=0.55, 1.11500201815e+000;x( 4)=0.32, y( 2)=0.60, 9.64607727216e-001; x( 4)=0.32, y( 3)=0.65, 8.20347369475e-001;x( 4)=0.32, y( 4)=0.70, 6.82447678179e-001; x( 4)=0.32, y( 5)=0.75, 5.51085208598e-001;x( 4)=0.32, y( 6)=0.80, 4.26392385902e-001; x( 4)=0.32, y( 7)=0.85, 3.084629956
27、33e-001;x( 4)=0.32, y( 8)=0.90, 1.97357129692e-001; x( 4)=0.32, y( 9)=0.95, 9.31056208594e-002;x( 4)=0.32, y(10)=1.00, -4.28599223403e-003; x( 4)=0.32, y(11)=1.05, -9.48339252969e-002;x( 4)=0.32, y(12)=1.10, -1.78572990364e-001; x( 4)=0.32, y(13)=1.15, -2.55553779055e-001;x( 4)=0.32, y(14)=1.20, -3.
28、25840150158e-001; x( 4)=0.32, y(15)=1.25, -3.89506988363e-001;x( 4)=0.32, y(16)=1.30, -4.46638204599e-001; x( 4)=0.32, y(17)=1.35, -4.97324951768e-001;x( 4)=0.32, y(18)=1.40, -5.41664032699e-001; x( 4)=0.32, y(19)=1.45, -5.79756479795e-001;x( 4)=0.32, y(20)=1.50, -6.11706288148e-001;x( 5)=0.40, y( 0
29、)=0.50, 1.49832105248e+000; x( 5)=0.40, y( 1)=0.55, 1.33499863207e+000;x( 5)=0.40, y( 2)=0.60, 1.17712512374e+000; x( 5)=0.40, y( 3)=0.65, 1.02502405502e+000;x( 5)=0.40, y( 4)=0.70, 8.78960023174e-001; x( 5)=0.40, y( 5)=0.75, 7.39145108704e-001;x( 5)=0.40, y( 6)=0.80, 6.05744871487e-001; x( 5)=0.40,
30、 y( 7)=0.85, 4.78883861067e-001;x( 5)=0.40, y( 8)=0.90, 3.58650625882e-001; x( 5)=0.40, y( 9)=0.95, 2.45102236196e-001;x( 5)=0.40, y(10)=1.00, 1.38268350928e-001; x( 5)=0.40, y(11)=1.05, 3.8154865070e-002;x( 5)=0.40, y(12)=1.10, -5.52528211681e-002; x( 5)=0.40, y(13)=1.15, -1.41986880814e-001;x( 5)=
31、0.40, y(14)=1.20, -2.22094439096e-001; x( 5)=0.40, y(15)=1.25, -2.95635232460e-001;x( 5)=0.40, y(16)=1.30, -3.62679511503e-001; x( 5)=0.40, y(17)=1.35, -4.23306164224e-001;x( 5)=0.40, y(18)=1.40, -4.77601036132e-001; x( 5)=0.40, y(19)=1.45, -5.25655426667e-001;x( 5)=0.40, y(20)=1.50, -5.67564743655e
32、-001;x( 6)=0.48, y( 0)=0.50, 1.73189274038e+000; x( 6)=0.48, y( 1)=0.55, 1.56203457721e+000;x( 6)=0.48, y( 2)=0.60, 1.39721691821e+000; x( 6)=0.48, y( 3)=0.65, 1.23780100674e+000;x( 6)=0.48, y( 4)=0.70, 1.08408753268e+000; x( 6)=0.48, y( 5)=0.75, 9.36322772315e-001;x( 6)=0.48, y( 6)=0.80, 7.94704449
33、054e-001; x( 6)=0.48, y( 7)=0.85, 6.59387198028e-001;x( 6)=0.48, y( 8)=0.90, 5.30487586840e-001; x( 6)=0.48, y( 9)=0.95, 4.08088685454e-001;x( 6)=0.48, y(10)=1.00, 2.92244201230e-001; x( 6)=0.48, y(11)=1.05, 1.82982206854e-001;x( 6)=0.48, y(12)=1.10, 8.03084940354e-002; x( 6)=0.48, y(13)=1.15, -1.57
34、904130516e-002;x( 6)=0.48, y(14)=1.20, -1.05344551621e-001; x( 6)=0.48, y(15)=1.25, -1.88398090610e-001;x( 6)=0.48, y(16)=1.30, -2.65007149319e-001; x( 6)=0.48, y(17)=1.35, -3.35237838904e-001;x( 6)=0.48, y(18)=1.40, -3.99164503887e-001; x( 6)=0.48, y(19)=1.45, -4.56868143302e-001;x( 6)=0.48, y(20)=
35、1.50, -5.08434993278e-001;x( 7)=0.56, y( 0)=0.50, 1.97122178640e+000; x( 7)=0.56, y( 1)=0.55, 1.79532959950e+000;x( 7)=0.56, y( 2)=0.60, 1.62406711323e+000; x( 7)=0.56, y( 3)=0.65, 1.45783058271e+000;x( 7)=0.56, y( 4)=0.70, 1.29695464975e+000; x( 7)=0.56, y( 5)=0.75, 1.14171810545e+000;x( 7)=0.56, y
36、( 6)=0.80, 9.92349533324e-001; x( 7)=0.56, y( 7)=0.85, 8.49032663329e-001;x( 7)=0.56, y( 8)=0.90, 7.11911352264e-001; x( 7)=0.56, y( 9)=0.95, 5.81094158922e-001;x( 7)=0.56, y(10)=1.00, 4.56658513233e-001; x( 7)=0.56, y(11)=1.05, 3.3865449139e-001;x( 7)=0.56, y(12)=1.10, 2.27108255770e-001; x( 7)=0.5
37、6, y(13)=1.15, 1.22025089193e-001;x( 7)=0.56, y(14)=1.20, 2.33922196376e-002; x( 7)=0.56, y(15)=1.25, -6.88187019710e-002;x( 7)=0.56, y(16)=1.30, -1.54649344213e-001; x( 7)=0.56, y(17)=1.35, -2.34152666459e-001;x( 7)=0.56, y(18)=1.40, -3.07391091913e-001; x( 7)=0.56, y(19)=1.45, -3.74434862348e-001;
38、x( 7)=0.56, y(20)=1.50, -4.35360556536e-001;x( 8)=0.64, y( 0)=0.50, 2.21566786369e+000; x( 8)=0.64, y( 1)=0.55, 2.03420113361e+000;x( 8)=0.64, y( 2)=0.60, 1.85695514362e+000; x( 8)=0.64, y( 3)=0.65, 1.68435816416e+000;x( 8)=0.64, y( 4)=0.70, 1.51677635240e+000; x( 8)=0.64, y( 5)=0.75, 1.35451904115e
39、+000;x( 8)=0.64, y( 6)=0.80, 1.19784408667e+000; x( 8)=0.64, y( 7)=0.85, 1.04696304942e+000;x( 8)=0.64, y( 8)=0.90, 9.02046083802e-001; x( 8)=0.64, y( 9)=0.95, 7.63226477663e-001;x( 8)=0.64, y(10)=1.00, 6.30604821954e-001; x( 8)=0.64, y(11)=1.05, 5.04252814597e-001;x( 8)=0.64, y(12)=1.10, 3.84216715
40、546e-001; x( 8)=0.64, y(13)=1.15, 2.70520476641e-001;x( 8)=0.64, y(14)=1.20, 1.63168572400e-001; x( 8)=0.64, y(15)=1.25, 6.21485581168e-002;x( 8)=0.64, y(16)=1.30, -3.25666193968e-002; x( 8)=0.64, y(17)=1.35, -1.21016534844e-001;x( 8)=0.64, y(18)=1.40, -2.03251399623e-001; x( 8)=0.64, y(19)=1.45, -2
41、.79330359558e-001;x( 8)=0.64, y(20)=1.50, -3.49319957540e-001;x( 9)=0.72, y( 0)=0.50, 2.46468422266e+000; x( 9)=0.72, y( 1)=0.55, 2.27805897940e+000;x( 9)=0.72, y( 2)=0.60, 2.09525125084e+000; x( 9)=0.72, y( 3)=0.65, 1.91671812800e+000;x( 9)=0.72, y( 4)=0.70, 1.74285462878e+000; x( 9)=0.72, y( 5)=0.
42、75, 1.57399842733e+000;x( 9)=0.72, y( 6)=0.80, 1.41043483523e+000; x( 9)=0.72, y( 7)=0.85, 1.25240175061e+000;x( 9)=0.72, y( 8)=0.90, 1.10009440963e+000; x( 9)=0.72, y( 9)=0.95, 9.53669851261e-001;x( 9)=0.72, y(10)=1.00, 8.13251055249e-001; x( 9)=0.72, y(11)=1.05, 6.78930742966e-001;x( 9)=0.72, y(12
43、)=1.10, 5.50774848504e-001; x( 9)=0.72, y(13)=1.15, 4.28825676973e-001;x( 9)=0.72, y(14)=1.20, 3.13104771740e-001; x( 9)=0.72, y(15)=1.25, 2.03615514033e-001;x( 9)=0.72, y(16)=1.30, 1.00345478241e-001; x( 9)=0.72, y(17)=1.35, 3.26856518657e-003;x( 9)=0.72, y(18)=1.40, -8.76530659133e-002; x( 9)=0.72
44、, y(19)=1.45, -1.72467247819e-001;x( 9)=0.72, y(20)=1.50, -2.51230220752e-001;x(10)=0.80, y( 0)=0.50, 2.71781110947e+000; x(10)=0.80, y( 1)=0.55, 2.52639950126e+000;x(10)=0.80, y( 2)=0.60, 2.33841138686e+000; x(10)=0.80, y( 3)=0.65, 2.15432937728e+000;x(10)=0.80, y( 4)=0.70, 1.97457455665e+000; x(10
45、)=0.80, y( 5)=0.75, 1.79951057910e+000;x(10)=0.80, y( 6)=0.80, 1.62944822055e+000; x(10)=0.80, y( 7)=0.85, 1.46465004375e+000;x(10)=0.80, y( 8)=0.90, 1.30533496765e+000; x(10)=0.80, y( 9)=0.95, 1.15168262131e+000;x(10)=0.80, y(10)=1.00, 1.00383741991e+000; x(10)=0.80, y(11)=1.05, 8.6191233228e-001;x
46、(10)=0.80, y(12)=1.10, 7.25992371111e-001; x(10)=0.80, y(13)=1.15, 5.96137711520e-001;x(10)=0.80, y(14)=1.20, 4.72386627914e-001; x(10)=0.80, y(15)=1.25, 3.54758095898e-001;x(10)=0.80, y(16)=1.30, 2.43254184181e-001; x(10)=0.80, y(17)=1.35, 1.37862222525e-001;x(10)=0.80, y(18)=1.40, 3.85567703264e-0
47、02; x(10)=0.80, y(19)=1.45, -5.46985959345e-002;x(10)=0.80, y(20)=1.50, -1.41949659709e-001;2. 选择过程的 k,sigma 的值：k=0; Sigma=1.44288077184e+002;k=1; Sigma=3.22090897364e+000;k=2; Sigma=4.65996003327e-003;k=3; Sigma=1.72117537914e-004;k=4; Sigma=3.30953429925e-006;k=5; Sigma=2.54137804427e-008;3. 达到精度要
48、求时的 k,sigma 以及 p(x,y)中的系数 c_rs(r = 0, 1,.,k; s = 0, 1,.,k)k = 5, sigma = 2.541378464155e-008c(0,0)= 2.02123051865e+000; c(0,1)=-3.66842679633e+000; c(0,2)= 7.09248619136e-001;c(0,3)= 8.48605406549e-001; c(0,4)=-4.15897436083e-001; c(0,5)= 6.74319952447e-002;c(1,0)= 3.19190900893e+000; c(1,1)=-7.41110377183e-001; c(1,2)=-2.69712460102e+000;c(1,3)= 1.63118340106e+000; c(1,4)=-4.84719972982e-001; c(1,5)= 6.06142812008e-002;c(2,0)= 2.56889811789e-001; c
