python bisection method

Elderdrinker answered on June 21, 2022 Popularity 9/10 Helpfulness 5/10

answer python bisection method

related Python Bisection Method

python bisection method

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def bisection(f, a, b, eps):
  if f(a) * f(b) >= 0:
    raise BaseException("Wrong interval!")
  if a > b:
    a, b = b, a
  n = 0
  x = (a + b) / 2
  while b - a >= 2*eps:
    if f(x) == 0:
      return x, n
    elif f(a) * f(x) < 0:
      b = x
    else:
      a = x
    x  = (a + b) / 2
    n += 1
  return x, n

Popularity 9/10 Helpfulness 5/10 Language python

Source: courses.fit.cvut.cz

Tags: bisection python

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Contributed on Jun 21 2022

Elderdrinker

0 Answers Avg Quality 2/10

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Python Bisection Method

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def bisection(f,a,b,N):
    '''Approximate solution of f(x)=0 on interval [a,b] by bisection method.

    Parameters
    ----------
    f : function
        The function for which we are trying to approximate a solution f(x)=0.
    a,b : numbers
        The interval in which to search for a solution. The function returns
        None if f(a)*f(b) >= 0 since a solution is not guaranteed.
    N : (positive) integer
        The number of iterations to implement.

    Returns
    -------
    x_N : number
        The midpoint of the Nth interval computed by the bisection method. The
        initial interval [a_0,b_0] is given by [a,b]. If f(m_n) == 0 for some
        midpoint m_n = (a_n + b_n)/2, then the function returns this solution.
        If all signs of values f(a_n), f(b_n) and f(m_n) are the same at any
        iteration, the bisection method fails and return None.

    Examples
    --------
    >>> f = lambda x: x**2 - x - 1
    >>> bisection(f,1,2,25)
    1.618033990263939
    >>> f = lambda x: (2*x - 1)*(x - 3)
    >>> bisection(f,0,1,10)
    0.5
    '''
    if f(a)*f(b) >= 0:
        print("Bisection method fails.")
        return None
    a_n = a
    b_n = b
    for n in range(1,N+1):
        m_n = (a_n + b_n)/2
        f_m_n = f(m_n)
        if f(a_n)*f_m_n < 0:
            a_n = a_n
            b_n = m_n
        elif f(b_n)*f_m_n < 0:
            a_n = m_n
            b_n = b_n
        elif f_m_n == 0:
            print("Found exact solution.")
            return m_n
        else:
            print("Bisection method fails.")
            return None
    return (a_n + b_n)/2

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Source: patrickwalls.github.io

Tags: python bisection

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Contributed on Oct 08 2023

Dmytro Skorobahat'ko

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python bisection method

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