Python question: def secant_method(f,x0,x1,tol,kmax): # YOUR CODE HERE raise NotImplementedError()

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Python question:
def secant_method(f,x0,x1,tol,kmax):
# YOUR CODE HERE
raise NotImplementedError()

Python Question Def Secant Method F X0 X1 Tol Kmax Your Code Here Raise Notimplementederror 1 (107.12 KiB) Viewed 47 times

Python Question Def Secant Method F X0 X1 Tol Kmax Your Code Here Raise Notimplementederror 2 (90.7 KiB) Viewed 47 times

Introduction The Secant Method can be used to find a root, Xx, of a function f(x) so that f(xx) = 0. This method is an adaptation of Newton's method, where the derivative is estimated using the approximation: f'(xk) – f(xk) – f(xk-1). Xk — Xk-1 In the Secant Method a sequence of successive estimates for Xx , labelled { xk}k>1, are calculated using the formula 1 Xk – Xk-1 Xk+1 = xk f(xk). f(xk) – f(xk-1) Geometrically Xk+1 is obtained from xk and Xx–1 by intersecting the straight line through (xx, f(xx)) and (xk+1, f(xx+1)) with the x-axis. Since each calculation of the new estimate, Xk+1, requires the values of the previous two estimates, xk and Xk-1, we must specify xo and xį initially, choosing values that are close to the root we seek. Ideally, we should choose xo and xı in a similar way to the initial endpoints of an interval for the bisection method, such that f(x) = 0 precisely once in the interval (x0, xi), though this is not necessary for the secant method to work. =
(a) [30 Marks] : Write a function, 'secant_method', which takes as input a function f, two real numbers to and xi, a positive real number tol and a positive integer kmax. This function should implement the Secant Method to find a root of a function f using the two starting points xo and X1. Successive estimates should be calculated until the relative error ek is less than tol or k > kmax: Recall that Xk – xk-1 ek Xk . • If no root is found an ArithmeticError should be raised. If tol < 0 then a ValueError sould be raised. If k max < 0 then a ValueError should be raised. If xo == xj then a ValueError should be raised. • Otherwise the function should return a tuple (xn, en, N) consisting of the final approximation, xn, the estimated relative error, en and the index of the approximation, N.