合肥工业大学计算方法源程序

#include <stdio.h> #include <math.h> double f(double x) { return 1 / (1 + pow(x, 2)); } double lagrangeInterpolation(double x[], double y[], int n, double point) { double result = 0.0; for (int i = 0; i <= n; i++) { double term = y[i]; for (int j = 0; j <= n; j++) { if (j != i) { term *= (point - x[j]) / (x[i] - x[j]); } } result += term; } return result; } double linearInterpolation(double x[], double y[], int n, double point) { int i; for (i = 0; i < n; i++) { if (point >= x[i] && point <= x[i + 1]) { break; } } double slope = (y[i + 1] - y[i]) / (x[i + 1] - x[i]); double result = y[i] + slope * (point - x[i]); return result; } int main() { double x[12]; // 11个等距插值节点 double y[12]; // 对应节点的函数值 double interval = 10.0 / 10.0; // 区间长度 double point1 = 0.5; // 预测点1 double point2 = 4.5; // 预测点2 // 计算插值节点和函数值 for (int i = 0; i <= 10; i++) { x[i] = -5.0 + i * interval; y[i] = f(x[i]); } // 计算拉格朗日插值并比较精确值和误差 double lagrangeResult1 = lagrangeInterpolation(x, y, 10, point1); double lagrangeResult2 = lagrangeInterpolation(x, y, 10, point2); double exactResult1 = f(point1); double exactResult2 = f(point2); double lagrangeError1 = fabs(lagrangeResult1 - exactResult1); double lagrangeError2 = fabs(lagrangeResult2 - exactResult2); printf("拉格朗日插值结果：\n"); printf("预测点 %.1f 的近似函数值：%.6f，精确值：%.6f，误差：%.6f\n", point1, lagrangeResult1, exactResult1, lagrangeError1); printf("预测点 %.1f 的近似函数值：%.6f，精确值：%.6f，误差：%.6f\n", point2, lagrangeResult2, exactResult2, lagrangeError2); // 计算分段线性插值并比较精确值和误差 double linearResult1 = linearInterpolation(x, y, 10, point1); double linearResult2 = linearInterpolation(x, y, 10, point2); double linearError1 = fabs(linearResult1 - exactResult1); double linearError2 = fabs(linearResult2 - exactResult2); printf("分段线性插值结果：\n"); printf("预测点 %.1f 的近似函数值：%.6f，精确值：%.6f，误差：%.6f\n", point1, linearResult1, exactResult1, linearError1); printf("预测点 %.1f 的近似函数值：%.6f，精确值：%.6f，误差：%.6f\n", point2, linearResult2, exactResult2, linearError2); return 0; }