数值分析作业C语言编程实现

1、K 10分用Romberg方法计算积分Z二的近似值。误差不趙过include include double f(double x)(double ans； ans=exp(x)；return ans；void meiinOdouble a=l,b=3,error=,t2020.htc；int i,j,k,m,n；h=b-a；t0 0=h*(f(a)+f(b)/2;k=l；wh i1e (1)t0k=0；m=l；for (j=0；jk-l；j+)m-m*2；for(i=l；i=m；i+)t0k=t0k+h*f(a+*h)；t0k = (t0 k+t0k-l)/2； for(j=l；j=k；j+)

2、 c=l；for (n=0；nj；n+)c=c*4；tjk-j=(c*tj-lk-j+l-tj-lk-j)/(c-l)； if(fabs(tk0-tk-10)error)(printf (Xn 积分结果 I a %lfn, tk 0);break；elseh=h/2;k+；积分结果I a 17.3672552、(10分)用简单迭代法求解方程 x=0,要求盼如|10二include include double f(double t)double ans；ans=pow(cos(t),3)；return ans；void main()double x=0,eslong=,xO；int N=20,

3、i；printf(Mn 近似初值 xO = %lfnx)；for(i=0;iN；i+)xO=x；x=f(x)；printf(w x%d = %lfn,i+l,x)；if (fabs(x-xO)eslong)break；if(fabs(x-xO)eslong)printf(M得到近似结果为x%lfnn,x,i);elseprintf (，r迭代失败n)；近似初值X0 = 0.000000xl = 1.000000x2 =队814477x3 =匕&82051x4 =匕859780x5 =8G7394x6 = 0SG4822x? = a.865695x8 = 0.8G5399x9 = 0.8&549

4、9 xi0 = 9.865465 xll = 0.865477 xl2 = 0.865473 xl3 = 0865474 xl4 = D865474得到近似结果为x Q 0-8654743、（10分）用四阶RK方法求初值问题的数值解取步长力=0丄计算结果取8位小数。y = l + .x20 11 MO) = o#include #include fdouble a=0,b=l.x,y=0,h=,kl,k2tk3.k4；int i.N；double f(double t,double s)double ans；ans=l+t*t；return ans；void main()N=(b-a)/h；k

5、x=a；printf (n 初值为(x0,y0) = ( %. 8f , %. 8f )n,x,y)； for(i=0；iN；i+)kl=f (xty)；k2=f(x+h/2,y+h*kl/2)；k3=f(x+h/2,y+h*k2/2)；k4=f(x+h,y+h*k3)；y=y+h*(kl+2*(k2+k3)+k4)/6；x=x+h；printf (H第d次输 出 结 果 为(x%df y%d)(%. 8f . %. 8f )n,i+lti+l,i+lfx,y)；1234567891書第第第第第第第第第2 ZL值ex出出出岀岀出出出出胡Cxl.yl)=c0-100000000.10033333

6、)x4.y4)=0.400000000.42133333)=0.500000000.54166667)=0.600003030.67200000)=0.800000000.9706666?0.900000001.14300000Cxie.yie = =0B-FB-Fa-T=:壬ja-vb-t%壬B-TCfi-K:三才 L士口士口士 口士 口士 口士 口止 口士 口士 口 y - 0 幺“幺幺幺幻广幺幺V-幺一岀4. （IQ分）已知函数表如下,用三次插值求X1.5）的近似值。XiL22,94.65.86,714.8433.7158.3679.2496.79include void main()d

7、ouble datax4=t,t,datay10=,13,x=,y； int i,j;y=0；for (i=0；i=3；i+)li=l;for(j=0；ji；j+)1 i = (x-dataxj)/(dataxi-dataxj)*l i； for(j=i+l；j=3； j+)1 i = (x-dataxj)/(dataxi-dataxj)*l i; y=y+datay i*l i:printfCXn f(x)在 x = %f 处的近似值为：y = %fnx,y)；FCx在 x = 1.508000 处的近似値为二 y = 17.7500805、（10分己知数据表如下.试求其最小二乘二次拟合名项

8、式Xi1.22.33.44.55.66.77.88.910.0yi11.714&721.443L3944.7361.4681.57105.11131.91include void main()double datay9=rint m=2,i.j.k；double ptdata94ta34,datax9 = ,for (i=0；i9；i+)for (j=l；j2*m+l；j+)dataij=l;for (k=O；kj;k+)dataij=dataij*dataxi;for(i=0；im+l; i+)for(j=0；jm+l；j+)aij=0；for(k=0；k9；k+)ai j=ai j+dat

9、ak i+j;a0 01=9；a0m+l=0；for(i=0；i9；i+)a0m+l=a0m+l+datayi；for (i=l；im+l;i+) aim+l=0;for(j=0；j9；j+)p=datay j:Ifor(k=0；ki;k+)p=p*dataxj:aim+l=aim+l+p；(9 000000)a0 + 50+ 354.840000)a2 = 504.180000(504000aa)aO * C354& al 23548.045200X2 = 31620.158300方程组的解为：a0 = 12.076541al = -2.000515a2 = 1.398707拟合多项式为：P

10、2 * C-2.000515x + 1.398707)x26、(20分)分别用列主元法和Jacobi迭代法求解方程组X - 2jc2 =31 一 2xt 十 - 3心=15一 X - 2x2 + 5工3 =10方程第1行互换位置后如下(一2000033)*1 亠(10+ -3.000000)x3 = 15.000000(1000000)x1 4 x2 + -1-000000)x3 = 3.000000x2 + C5-000000)x3 = 1.0000000 方程经：次消元如下一2000000dL *- x2 x3 = 15.0600000000000xl + x2 * x3 = 10.500

11、0000000000xl *- x2 * x3 = 2.500000方程第2行互换位萱后如下xl * x2 x3 = 15.000000xl + x2 * x3 = 2.500000xl + x2 * C-2.500000x3 = 10.500000 方程经2次消元如下一2000000)x1 十 C10+ (-3.000000)x3 = 150000000.000000)x1 十 x2 * C6.500000x3 = 2-500000xl 十 x2 + C0.285714x3 = 11.571429 方程化简得(一2 000000)x1 十 C10+ x3 = 2-5B0000(0000000

12、)x1 * (0000000x2 + C0.285714)x3 = 11.571429方程组的解为：X1=118.000000x2=37.250000x3=40.500000fni+l,ai)；elseprintf (迭代失败n)；化为b矩阵如下0000000 2000000 1.000000 3.0000000.200000 9.000000 0.300000 1.5000000.200000 0.400000 0.000000 2.000000计算结果为xl = 118 网x2 = 37.250x3 = 40L 500现场考试题目1#include includedouble f(doub

13、le x)double ans；ans=exp(x)；return(ans)；void main()doub 1 e a=-l,b=l,error= ,in=lh,T0T.F；int k；h=(b-a)/2；T0=h*(f(a)+f(b)；while(l)F二 0；for(k=l；k=pow,m-1)；k+)F=F+f(a+(2*k-l)*h)；T二T0/2+h*F；if (fabs(T-TO)error)break；m+；h=h/2；TO 二T；printfC积分结果为I%fnT）； 题目2#include double f(double t.double s)double ans；ans=l+t*t；return (ans)；void main()(doubl