1 割线法
割线法用于求方程 f(x) = 0 的根。它是从根的两个不同估计 x1 和 x2 开始的。这是一个迭代过程，包括对根的线性插值。如果两个中间值之间的差值小于收敛因子，则迭代停止。
亦称弦截法，又称线性插值法.一种迭代法.指用割线近似曲线求方程根的2步迭代法.此法用通过点(xk，f(xk))及(xk-1，f(xk-1))的割线
近似曲线y=f(x)，用割线的根作为方程根的新近似xk+1，从而得到方程求根的割线法迭代程序
( k=1，2，…，n)，
其中x0，x1为初始近似.若f(x)在根x*的邻域内有二阶连续导数，且f′(x*)≠0，则当x0，x1在x*邻域内时，割线法收敛于x*，其收敛阶为
2 源程序
using System;
using System.Text;
using System.Collections;
using System.Collections.Generic;
namespace Legalsoft.Truffer.Algorithm
{
public delegate double delegateFunctionX(double x);
public static partial class Algorithm_Gallery
{
public static delegateFunctionX funx = null;
public static bool Secant(double x1, double x2, out double x0, double Epsilon)
{
int n = 0;
double xm;
x0 = x1;
if (funx(x1) * funx(x2) < 0)
{
do
{
x0 = (x1 * funx(x2) - x2 * funx(x1)) / (funx(x2) - funx(x1));
double c = funx(x1) * funx(x0);
x1 = x2;
x2 = x0;
n++;
if (Math.Abs(c) < float.Epsilon)
{
break;
}
xm = (x1 * funx(x2) - x2 * funx(x1)) / (funx(x2) - funx(x1));
} while (Math.Abs(xm - x0) >= Epsilon);
return true;
}
else
{
return false;
}
}
}
}
3 源代码
using System;
using System.Text;
using System.Collections;
using System.Collections.Generic;namespace Legalsoft.Truffer.Algorithm
{public delegate double delegateFunctionX(double x);public static partial class Algorithm_Gallery{public static delegateFunctionX funx = null;public static bool Secant(double x1, double x2, out double x0, double Epsilon){int n = 0;double xm;x0 = x1;if (funx(x1) * funx(x2) < 0){do{x0 = (x1 * funx(x2) - x2 * funx(x1)) / (funx(x2) - funx(x1));double c = funx(x1) * funx(x0);x1 = x2;x2 = x0;n++;if (Math.Abs(c) < float.Epsilon){break;}xm = (x1 * funx(x2) - x2 * funx(x1)) / (funx(x2) - funx(x1));} while (Math.Abs(xm - x0) >= Epsilon);return true;}else{return false;}}}
}
