给定函数的Chebyshev逼近

本文主要是介绍给定函数的Chebyshev逼近，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

//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();
}

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