1.拉格朗日插值多项式 ，用于离散数据的拟合
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#include < stdio.h > #include < conio.h > #include < alloc.h > float lagrange( float * x, float * y, float xx, int n) /* 拉格朗日插值算法 */ { int i,j; float * a,yy = 0.0 ; /* a作为临时变量，记录拉格朗日插值多项式 */ a = ( float * )malloc(n * sizeof ( float )); for (i = 0 ;i <= n - 1 ;i ++ ) { a[i] = y[i]; for (j = 0 ;j <= n - 1 ;j ++ ) if (j != i) a[i] *= (xx - x[j]) / (x[i] - x[j]); yy += a[i]; } free(a); return yy; } main() { int i,n; float x[ 20 ],y[ 20 ],xx,yy; printf( " Input n: " ); scanf( " %d " , & n); if (n >= 20 ) {printf( " Error!The value of n must in (0,20). " ); getch(); return 1 ;} if (n <= 0 ) {printf( " Error! The value of n must in (0,20). " ); getch(); return 1 ;} for (i = 0 ;i <= n - 1 ;i ++ ) { printf( " x[%d]: " ,i); scanf( " %f " , & x[i]); } printf( " /n " ); for (i = 0 ;i <= n - 1 ;i ++ ) { printf( " y[%d]: " ,i);scanf( " %f " , & y[i]);} printf( " /n " ); printf( " Input xx: " ); scanf( " %f " , & xx); yy = lagrange(x,y,xx,n); printf( " x=%f,y=%f/n " ,xx,yy); getch(); }