Fixed point iterations, The equation x

Fixed point iterations

Reference no: EM13123252

1. The equation x - 3 ln x = 2 has exactly two solutions A and B, with 0 < A < B.

(You do not have to show this.)

(a) Show that A is in [0.5,0.7], and B is in [8.3,8.5].

(b) Consider the following fixed-point iteration for finding a solution of the given equation: xn+1 = e(1/3(Xn-2)):

Show that if X0 = B+ E, where E is a positive real number, then X1 > X0. Deduce that this Fixed point iteration does not converge to ¯Before all X0 > B. (Hint: You may need to use the facts that B is a solution of x-3 ln x = 2, and that B> 3.)

Xn+1 = 2 + 3 ln Xn:

(i) Show that this fixed point iteration converges to B for all X0 is in [6.5,9.5].

(ii) The equation x - 3 ln x = 2 has exactly two solutions A and B, with 0 < A < B.

Reference no: EM13123252

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