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2. [10 pts ] Use fixed-point iteration to determine a solution accurate to within 10-3 for f(x) x...
3. Use Newton's method to find solution accurate to within 10-3 for x3 + 3x2 – 1 = 0 on (-3,-2]. Use po -2,5. 4. Use Secant method to find the solution P4 for In(x - 1) + cos(x - 1) = 0 on [1.3,2]. Use po 1.3 and p1 = 1.5. 5. Use False position method to find the solution P4 for 3x – e* = 0 on [1,2]. Use - Ро 1 and P1 2.
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.
Find all the zeros of f (x) = x2 +10 cosx by using the fixed-point iteration method for an appropriate iteration function g. Find the zeros accurate to within 10-4.
2. (25 pts) Consider the fixed point problem with g(x) 3 Use the fixed point theorem to show fixed point iterations using g(r) converge to fixed point p E (0, 1] for all initial guesses po E [0, 1]. a Remember, the fixed point theorem: If g(x) is continuously differentiable in [a, b] and g [a, b g(x) converge to a fixed point p E [a, b] for all initial guesses po E [a, b. a, band g (x k...
(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.
Predict the roots of the polynomial f(x)=x^3-6x^2+11x-6 writing a code. Show your code and print the iterative steps. Use a) Fixed Point Iteration and b) Newton Raphson. The initial values and the convergence criteria are up to you.
Predict the roots of the polynomial f(x)=x^3-6x^2+11x-6 writing a code. Show your code and print the iterative steps. Use a) Fixed Point Iteration and b) Newton Raphson. The initial values and the convergence criteria are up to you.
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...
2a², where [Fixed Point Iterations, 15 pts). Let g(2) = -22 + 3x + a a is a parameter. (a) Show that a is a fixed point of g(x). (b) For what values of a does the iteration scheme On+1 = g(n) converge linearly to the fixed point a (provided zo is chosen sufficiently close to a)? (c) Is there a value of a for which convergence is quadratic?