Kindly go through the solution provided below.
(a) Draw the first two iterations of the Bisection method for finding the root of the...
Program for the bisection method for finding the root of the nonlinear equation with a programming language(Matlab)
1) Use the bisection method to find the third approximation of 2 starting with the initial interval [1,2], and find the corresponding absolute error. Also, compute the number of iterations needed to achieve an approximation accurate to within 10 Then, use the suitable one to compute the second approximation of the root using xo,and find an upper bound for the corresponding error. 1) Use the bisection method to find the third approximation of 2 starting with the initial interval [1,2],...
2. (a) the bisection method for finding a zero of a function fR-R starts with an initial interval of length 1, what is the length of the interval containing the root after six iterations? (b) If the root being sought is r, such that f'(r.)0, how does this affect the convergence rate of the bisection method?
Newton's method is always the slowest algorithm (takes the most iterations) for finding a root. True O False The shape of the function influences the performance of the False Position Method. O True O False The Bisection Method can fail to converge if f (201) a and f (xu) have opposite signs. True False
Write a Matlab function for: 1. Root Finding: Calculate the root of the equation f(x)=x^3 −5x^2 +3x−7 Calculate the accuracy of the solution to 1 × 10−10. Find the number of iterations required to achieve this accuracy. Compute the root of the equation with the bisection method. Your program should output the following lines: • Bisection Method: Method converged to root X after Y iterations with a relative error of Z.
ONLY ANSWER IN MATLAB. 11. Find a bound for the number of Bisection method iterations needed to achieve an approximation with accuracy 10-3 to the solution of x³ +x – 4 = 0 lying in the interval (1, 4]. Find an approximation to the root with this degree of accuracy. please solve in MATLAB.
Q2. Use two iterations of the bisection method to find the root of f)10x2 +5 that lies in the interval (0.6, 0.8). Evaluate the approximate error for each iteration. (33 points)
I need to find approximate error for the first 5 iterations. The question says using bisection method find the root, f(x) = (x^3)+(2x)-6 . Xl=0.4 . Xu=1.8. Use 6 decimal digits in calculations. (I have already done 5 root iterations, I have no clue how to find approximate error though.)
Using the Bisection method, find an approximate root of the equation sin(x)=1/x that lies between x=1 and x=1.5 (in radians). Compute upto 5 iterations. Determine the approximate error in each iteration. Give the final answer in a tabular form.
5. For each of the following functions, and the corresponding initial interval, tell whether Bisection method can be applied to find a root in the interval, and if so, how many iterations are required to achieve the associated accuracy. Recall 10-G1 (b-a). (a) f(x) = sin(x), [-1, 1], E = 2-16 (b) f(x) = sn'(x), [-1, 1], € = 2-16 (c) f(z) = cos(x), [-1, 1], ε = 2-16 7. Show that Newton's method for finding the root of a...