The Newton-Raphson method

Newton-Raphson方法解析

原创于 2020-08-03 15:57:03 发布 · 241 阅读

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本文深入探讨了Newton-Raphson方法，一种用于求解非线性方程的有效数值解法。通过Python实现该方法，详细解释了其工作原理及应用实例，展示了如何通过迭代逼近根的精确位置。

"""The Newton-Raphson method"""
def newton(f,df,x,tol=0.001,maxiter=100):
    """
    f:the function to solve
    df:the derivative function of f
    x:initial guess value of x
    tol:the precision of the solution
    maxiter:max number of interations
    return:the x-axis value of the root,
    number of interations used
    """
    n=1
    while n <= maxiter:
        x1 = x-f(x)/df(x)
        if abs(x1-x) < tol:
            return x1,n
        else:
            x=x1
            n=n+1
    return None,n
"""for example"""
y = lambda x:x**3 +2.0*x**2-5
dy = lambda x:3*x**2+4*x
root,interations = newton(y,dy,5.0,0.00001,100)
print("root is:",root)
print("interations is",interations)