Find the smallest positive root for the given function by using the bisection method with accuracy...
Using MATLAB or FreeMat ---------------------------- Bisection Method and Accuracy of Rootfinding Consider the function f(0) = 3 cos 2r cos 4-2 cos Garcos 3r - 6 cos 2r sin 2r-5.03r +5/2. This function has exactly one root in the interval <I<1. Your assignment is to find this root accurately to 10 decimal places, if possible. Use MATLAB, which does all calculations in double precision, equivalent to about 16 decimal digits. You should use the Bisection Method as described below to...
5. Use bisection to find the smallest positive root of each of the following functions: a. cos(3x) +1e
1 Find the root of f(x) = x3-3 using the bisection method on the interval [1,2]. (Do three iterations). GatvEN ()5 1.5 (4) Cls .5).375 40 zor ( han R(1.25) 1.04675 1.2s fi.a) LS1-Ge1 1a5 1.25
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2 + 14x – 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos X – X. (a). Approximate a root of f(x) using Fixed- point method accurate to within 10-2 . (b). Approximate a root of f(x) using Newton's method accurate to within 10-2. Find the second Taylor polynomial P2(x) for the function f(x) =...
Question 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2 for x3 - 7x2 + 14x - 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos x - x. (a). Approximate a root of f(x) using Fixed-point method accurate to within 10-2 (b). Approximate a root of f(x) using Newton's method accurate to within 10-2.
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.
Find the root of f(x) = ex- a. Using incremental search method. b. Using bisection method. c. Compare the processing time of two methods for error of less than 0.01%. d. Compare the error for 20 iterations between the two methods.
[USING R] Write a function bisect(f, lower, upper, tol = 1e-6) to find the root of the univariate function f on the interval [lower, upper] with precision tolerance =< tol (defaulted to be 10-6 ) via bisection, which returns a list consisting of root, f.root (f evaluated at root), iter (number of iterations) and estim.prec (estimated precision). Apply it to the function f(x) = x3 - x - 1 on [1, 2] with precision tolerance 10-6 . Compare it with...
An algorithm for the Bisection method function root Bisect ( x,, x, e, imax) while i s imax x' ←(x, +x.)/2 [or 1. ← f(x.) if f. = 0 or (x,-x,) x,+(x,-x,)/2] /r +x, then root ←x exit end if ii +1 if f, × f, < 0 then else end if end while root 'failed to converge"
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.