张扬 2010212420数值计算方法实验.docVIP

实验一 插值法 算法设计思想: 在插值计算中，取样点的多少往往会影响所得插值函数优化程度。一般情况下，取样点越多所得插值函数越优化，对应的函数值与标准函数值越接近。 在MATLAB中实现分段线性插值，分段二次插值，拉格朗日插值的命令为interp1,其格式: Y1=interp1(X,Y,X1，’method’) 函数根据X,Y的值，计算函数在X1处的值。X,Y是两个等长的已知向量，分别描述采样点和样本值，X1是一个向量或标量，描述欲插值点，Y1是一个与X1等长的插值结果。 程序清单： 分段线性插值 #includestdio.h #includemath.h double Lagrange2(double *x, double *y, double input) { double output; int i; for (i=0;i5;i++) { if (x[i] = input x[i+1] = input) { output=y[i] +(y[i+1]-y[i])*(input-x[i])/(x[i+1]-x[i]); break; } } return output; } 2.分段二次插值 double Lagrange3(double *x,double *y,double u) { int i,k=0; double v; for(i=0;i6;i++) { if(ux[1]) { k=0; v=y[k]*(u-x[k+1])*(u-x[k+2])/((x[k]-x[k+1])*(x[k]-x[k+2]))+y[k+1]*(u-x[k])*(u-x[k+2])/((x[k+1]-x[k])*(x[k+1]-x[k+2]))+y[k+2]*(u-x[k])*(u-x[k+1])/((x[k+2]-x[k])*(x[k+2]-x[k+1])); } if((x[i]uu=x[i+1])(fabs(u-x[i])=fabs(u-x[i+1]))) { k=i-1; v=y[k]*(u-x[k+1])*(u-x[k+2])/((x[k]-x[k+1])*(x[k]-x[k+2]))+y[k+1]*(u-x[k])*(u-x[k+2])/((x[k+1]-x[k])*(x[k+1]-x[k+2]))+y[k+2]*(u-x[k])*(u-x[k+1])/((x[k+2]-x[k])*(x[k+2]-x[k+1])); } if ((x[i]uu=x[i+1])fabs(u-x[i])fabs(u-x[i+1])) { k=i; v=y[k]*(u-x[k+1])*(u-x[k+2])/((x[k]-x[k+1])*(x[k]-x[k+2]))+y[k+1]*(u-x[k])*(u-x[k+2])/((x[k+1]-x[k])*(x[k+1]-x[k+2]))+y[k+2]*(u-x[k])*(u-x[k+1])/((x[k+2]-x[k])*(x[k+2]-x[k+1])); } if(ux[4]) { k=3; v=y[k]*(u-x[k+1])*(u-x[k+2])/((x[k]-x[k+1])*(x[k]-x[k+2]))+y[k+1]*(u-x[k])*(u-x[k+2])/((x[k+1]-x[k])*(x[k+1]-x[k+2]))+y[k+2]*(u-x[k])*(u-x[k+1])/((x[k+2]-x[k])*(x[k+2]-x[k+1])); } } return v; } void main() { double x[6] = {0.0, 0.1, 0.195, 0.3, 0.401, 0.5},y[6] = {0.39894,0.39695,0.39142,0.38138,0.36812,0.35206}; double u; scanf(%lf,u); 拉格朗日插值： double Lagrange1(double *x, double *y, double xx) { int i,j; double *a,yy=0.000; a=new double[6]; for(i=0;i 6;i++) { a[i]=y[i]; for(j=0;j 6;j++) if(j!=i) a[i]*=(xx-x[j])/(x[i]-x[j]); yy+=a[i]; } delete a; return yy; } double Lagrange2(double *x