Determine the root of f(x)= e^x-2x-1 using fixed point iteration with initial value of 1.0 ?
Determine the root of f(x)= e^x-2x-1 using fixed point iteration with initial value of 1.0 ?
3) Use simple fixed-point iteration to locate the root of f(x) = 2 sin(x) - x Use an initial guess of Xo = 0.5 and iterate until Eg s 0.001%. Verify that the process is linearly convergent.
1. Determine the root of function f(x)= x+2x-2r-1 by using Newton's method with x=0.8 and error, e=0.005. 2. Use Newton's method to approximate the root for f(x) = -x-1. Do calculation in 4 decimal points. Letx=1 and error, E=0.005. 3. Given 7x)=x-2x2+x-3 Use Newton's method to estimate the root at 4 decimal points. Take initial value, Xo4. 4. Find the root of f(x)=x2-9x+1 accurate to 3 decimal points. Use Newton's method with initial value, X=2
3. (30 pts) (Problem 6.2) Determine the highest real root of f(x) 2x3- 11.7x2 + 17.7x -5 a) Graphically. b) Write a MATLAB program using the fixed-point method to determine the root with xo- Write a MATLAB program using the Newton-Raphson method to determine the root with Xo-3. c) d) Write a MATLAB program using the secant method to determine the root with x-1-3 and Xo- 4. e) Compare the relative errors between these three methods at the third iteration...
4) (16 points) The function f(x)= x? – 2x² - 4x+8 has a double root at x = 2. Use a) the standard Newton-Raphson, b) the modified Newton-Raphson to solve for the root at x = 2. Compare the rate of convergence using an initial guess of Xo = 1,2. 5) (14 points) Determine the roots of the following simultaneous nonlinear equations using a) fixed-point iteration and b) the Newton-Raphson method: y=-x? +x+0,75 y + 5xy = r? Employ initial...
(4) You are asked to solve for the root of the following equation with fixed-point iteration: Determine the solution approach that converges for initial guesses in the range of 0 < z < 7. Use either a graphical or analytical approach to prove that your formulation always converges in the given range.
2. (a) Suppose we have to find the root xof x); that is, we have to solve )0. Fixed-point methods do this by re-writing the equation in the form x·= g(x*) , and then using the iteration scheme : g(x) Show this converges (x-→x. as n→o) provided that K < 1 , for all x in some interval x"-a < x < x*+a ( a > 0 ) about the rootx 6 points] (b) Newton's method has the form of...
6.5 Employ the Newton-Raphson method to determine a real root for 4x20.5 using initial guesses of (a) 4.52 f(x) 15.5x Pick the best numerical technique, justify your choice and then use that technique to determine the root. Note that it is known that for positive initial guesses, all techniques except fixed-point iteration will eventually converge. Perform iterations until the approximate relative error falls below 2 %. If you use a bracket- ing method, use initial guesses of x 0 and...
2. [10 pts ] Use fixed-point iteration to determine a solution accurate to within 10-3 for f(x) x - cos(x)/2, for x in [ 0,1]. Use your calculator to calculate values, but be sure to show what values are being calculated. (a) show the function g(o) that you use: (b) show the initial value po that you use: (c) show the computations for the successive values of the pi until convergence: 2. [10 pts ] Use fixed-point iteration to determine...
Find the fixed point of e-e' to within 0.1 by using fixed point iteration.
Use the Newton-Raphson method to find the root of f(x) = e-*(6 - 2x) - 1 Use an initial guess of xo = 1.2 and perform 3 iterations. For the N-R method: Xi+1 = x; - f(x;) f'(x;)