问题描述
我对Durand-Kerner-Method(https://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method)的实现似乎无效。我相信(请参见以下代码)我在算法部分本身中未正确计算新的近似值。我似乎无法解决该问题。非常感谢您提供任何建议。
#include <complex>
#include <cmath>
#include <vector>
#include <iostream>
#include "DurandKernerWeierstrass.h"
using namespace std;
using Complex = complex<double>;
using vec = vector<Complex>;
using Matrix = vector<vector<Complex>>;
//PRE: Recieves input value of polynomial,degree and coefficients
//POST: Outputs y(x) value
Complex Polynomial(vec Z,int n,Complex x) {
Complex y = pow(x,n);
for (int i = 0; i < n; i++){
y += Z[i] * pow(x,(n - i - 1));
}
return y;
}
/*PRE: Takes a test value,degree of polynomial,vector of coefficients and the desired
precision of polynomial roots to calculate the roots*/
//POST: Outputs the roots of Polynomial
Matrix roots(vec Z,int iterations,const double precision) {
Complex z = Complex(0.4,0.9);
Matrix P(iterations,vec(n,0));
Complex w;
//Creating Matrix with initial starting values
for (int i = 0; i < n; i++) {
P[0][i] = pow(z,i);
}
//Durand Kerner Algorithm
for (int col = 0; col < iterations; col++) {
*//I believe this is the point where everything is going wrong*
for (int row = 0; row < n; row++) {
Complex g = Polynomial(Z,n,P[col][row]);
for (int k = 0; k < n; k++) {
if (k != row) {
g = g / (P[col][row] - P[col][k]);
}
}
P[col][row] -= g;
}
return P;
}
}
以下代码是我用来测试该功能的代码:
int main() {
//Initializing section
vec A = {1,-3,3,-5 };
int n = 3;
int iterations = 10;
const double precision = 1.0e-10;
Matrix p = roots(A,iterations,precision);
for (int i = 0; i < iterations; i++) {
for (int j = 0; j < n; j++) {
cout << "p[" << i << "][" << j << "] = " << p[i][j] << " ";
}
cout << endl;
}
return 0;
}
重要的是要注意Durand-Kerner-Algorithm连接到此代码中未包含的头文件。
解决方法
您的问题是您没有将新值转录到索引为col+1
的下一个数据记录中。因此,在下一个循环中,您将从零项的数据集重新开始。更改为
P[col+1][row] = P[col][row] - g;
如果您想立即对所有后续近似值使用新的改进近似值,请使用
P[col+1][row] = (P[col][row] -= g);
然后,所有数据集都包含下一个近似值,尤其是第一个近似值将不再包含初始设置的幂。