C++_数值分析_三次样条插值_自动选取步长梯形法_Romberg求积法_列主元高斯消去法_列主元LU分解法_Jacobi迭.docx

《C++_数值分析_三次样条插值_自动选取步长梯形法_Romberg求积法_列主元高斯消去法_列主元LU分解法_Jacobi迭.docx》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、数值分析上机实验报告之样条插值1.三次样条插值（初值条件1）：P52.9、给定函数y=fx的函数表和边界条件s''75=0，s''80=0，求三次样条插值函数s(x)，并求f(78.3)的近似值。函数表x757677787980y=fx2.7682.8332.9032.9793.0623.153源代码：yangtiao.cpp#include#includevoidmain(){intchoice=0;intn=2;doublexx,*x,*y,*a,*b,*a1,*b1,*h,*m;cout<<"请输入插

2、值节点个数n："<>n;x=newdouble[n];y=newdouble[n];a=newdouble[n];b=newdouble[n];a1=newdouble[n];b1=newdouble[n];h=newdouble[n-1];m=newdouble[n+1];cout<<"请输入"<>x[i]>>y[i];}for(intj=0;j

3、点xx："<>xx;cout<<"请选择边界条件："<>choice;switch(choice){case1:{doubletemp1,temp2;a[0]=0;a[n-1]=1;cout<<"请输入边界条件的两个一阶微商值s'(x1)与s'(xn)："<>temp1>>temp2;b[0]=2*temp1;b[n-1]=2*temp2;break;}case2:{a[0]=1;a[n-1]=0;b[0]=3/h[0]*(y[1]-y[0]);b[n-1]=3/h[n-2]*(y[n-

4、1]-y[n-2]);break;}}for(intk=1;k

5、n-1;j>=0;j--){m[j]=a1[j]*m[j+1]+b1[j];}//判别xx所在区间并输出结果cout<<"插值结果为：";for(k=0;kxx){doubleoutput=0;output=(1+2*(xx-x[k])/(x[k+1]-x[k]))*pow(((xx-x[k+1])/(x[k]-x[k+1])),2)*y[k]+(1+2*(xx-x[k+1])/(x[k]-x[k+1]))*pow(((xx-x[k])/(x[k+1]-x[k])),2)*y[k+1

6、]+(xx-x[k])*pow(((xx-x[k+1])/(x[k]-x[k+1])),2)*m[k]+(xx-x[k+1])*pow(((xx-x[k])/(x[k+1]-x[k])),2)*m[k+1];cout<

7、数s(x)，并求f(0.35)的近似值。函数表x0.250.30.390.450.53y=fx0.50.54770.62450.67080.728源代码：yangtiao.cpp(同上)运行结果截图：3.自动选取步长梯形法：P977、使用自动选取步长梯形法计算积分0121+t2dt的近似值。（给定ε=0.01）源代码：SelfSelLength.cpp#include#includedoublefun(doublea){return2/(1+a*a);}doubleSelfSelLength(doubleR

8、_a,doubleR_b,doublee){doubleh=(R_b-R_a)/2;doubleR1=(fun(R_a)+fun(R_b