Use the Bisection Method to locate a root of e* = cos(x)+0.25 Choose one of the given intervals [1, 1+0.3k], [0, 0+0.3k], [2, 2+0.3k] as the initial guess and explain your choice. Estimate the number of iterations needed to find the root within an accuracy of 10“. Then compute 5 iterations and record your calculations in the table below. Iteration XI Xu Xr 3 1 2 3 4 5

Use the Bisection Method to locate a root of e* = cos(x)+0.25 Choose one of the given intervals [1, 1+0.3k], [0, 0+0.3k], [2, 2+0.3k] as the initial guess and explain your choice. Estimate the number of iterations needed to find the root within an accuracy of 10“. Then compute 5 iterations and record your calculations in the table below. Iteration XI Xu Xr 3 1 2 3 4 5

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.5: Iterative Methods For Solving Linear Systems

Problem 21EQ

See similar textbooks

Similar questions

How many iterations are needed to obtain the root of f(x) = 3x + cos2x if the bracket is (-0.5, 0) and the false position method is used? Initial approximation should be counted as one iteration. Round off your approximations to 3 decimal places.
Use bisection method to locate the root f(x)=7sin(x)e^(-x) - 1 on a closed interval [0,1]. Use 12 iterations to extract the root.
Find the positive root of x -cos x = 0by iteration and regulafalsi method.
Find the root between (2,3) of x3+ - 2x - 5 = 0, by using regular falsi method correct to three decimal places.
Find an approximation to √ 3 correct to within 10^(−4) using the FixedPoint iteration. Compare your result and the number of iterations required with the answer obtained using the Bisection Algorithm
It is easy to observe that root of f(x) = x^2 −8 lies in the interval [2, 3]. Use Bisection methodto find the root. How many iterations are required in order to within 0.001953125 of the root.
Assuming an initial bracket of (-0.5, 0), what is the approximate value of the root of f(x) = 3x + cos2x after two iterations of the false position method? Initial approximation should be counted as one iteration.
Solve the approximate root of f(x) = x^5 - 3 using at least 5 iterations on Bisection Method with range from a = 0 and b = 10.
Assuming that the halving method starts with the interval [10,15], 10-30 relative How many steps must be taken to calculate a root with precision?
Find one real root of ln(x^4) = 0.70 using five iterations of bisection method on the interval (0.5,2)
What is the second iterative value of the root f(x) = x2 - 3. with the initial bracket [1, 2] using bisection method
1. Use the Intermediate Value Theorem to nd an interval of length one that contains a root of f(x) = sin2(x) - x - ex. Then write the iterations of Bisection method to an approximate root of f(x) within 1/8 accuracy.