Newton’s method (or Newton-Raphson method) is a root-finding
algorithm. It solves
equations of the form, 𝑓(𝑥)=0 starting from an initial guess, 𝑥0
and iteratively updating the
solution at step 𝑖+1 according to until convergence i.e.,
|𝑥𝑖+1 −𝑥|<𝜖 (𝜖 is a small positive
number):
- Please Use Matlab Newton S Method Or Newton Raphson Method Is A Root Finding Algorithm It Solves Equations Of The 1 (2.43 KiB) Viewed 45 times
Here, x; is the solution at itħ iteration and denotes differentiation wrt. x. The following is a pseudocode for Newton's method: dx Inputs: Evaluation functions for f(x) and f'(x) = Initial guess, xo (make sure f'(x) = 0) Maximum iterations, imax Tolerance, e procedure Newtons Method(f, df, xo, imax, E) if f(xo/<e then return xo X; = xo for i = 0, 1, 2, ---, imax do Xi+1 = x; -f(x)/f'(xi) if Xi+1 – xil< e then return Xi=1 X; = Xi=1 print "Max Iterations reached” Implement Newton's method in Matlab as outlined in the pseudocode and use it to solve the following equations (40 + 10 + 20 pts): a e-2 = 4 b. x3 - 6x2 + 11x - 6 = 0 For this part, run the procedure with initial guesses starting from 0 to 5 in steps of 0.5 and add your observations in a comment in the Matlab file. Plot f(x) and the solution(s) you obtained for both cases and graphically verify your solution for both parts. Choose appropriate limits for the x- and y-axes.