给定函数的Chebyshev逼近

来源：互联网发布：淘宝联盟2016 编辑：程序博客网时间：2024/06/11 09:54

//计算给定函数的Chebyshev逼近
#include <iostream>
#include <math.h>
#include <fstream>
#include <iomanip>

using namespace std;

const double pi = 3.141592653589793;

class chebyshev
{
private:
int div, i, j, n;
double a, b, func, F, sum, t0, t1, temp, x, y;
double *c, *f;

public:
chebyshev()
{
  div = 10;
}
double function(double z)
{
  func = sin(z) * z * z * (z * z - 2);
  return func;
}
void cheb_coeff();
void cheb_eval();
~chebyshev()
{
  delete[] c, f;
}
};

void main()
{
chebyshev cheby;
cheby.cheb_coeff();
}

//计算逼近多项式的系数
void chebyshev::cheb_coeff()
{
cout << "\n输入n：";
cin >> n;
c = new double[n];
f = new double[n];
cout << "\n输入区间下限和上限（即a和b）";
cin >> a >> b;
for (i = 0; i < n; i++)
{
  y = cos(pi * (i + 0.5) / n);
  x = 0.5 * y * (b - a) + 0.5 * (b + a);
  f[i] = function(x);
}
for (i = 0; i < n; i++)
{
  sum = 0.0;
  for (j = 0; j < n; j++)
  {
   sum += f[j] * cos(pi * i * (j + 0.5) / n);
  }
  c[i] = 2 * sum / n;
  cout << "\nc[" << i << "] = " << c[i] << endl;
}
cheb_eval();
}

void chebyshev::cheb_eval()
{
ofstream fout("chebyshev.txt");
x = a;
for (i = 0; i <= div; i++)
{
  y = (2 * x - a - b) / (b - a);
  t0 = 1.0;
  t1 = y;
  F = c[1] * t1 + 0.5 * c[0];
  for (j = 2; j < n; j++)
  {
   temp = t1;
   t1 = 2 * y * t1 - t0;
   t0 = temp;
   F += c[j] * t1;
  }
  fout << x << setw(15) << F << endl;
  x += (b - a) / div;
}
fout.close();
}