Analysis and Methods Clear writing, please ? **Fixed-Point Iteration Exercise****Problem Statement:**1. Solve by fixed-point iteration:\[ x^4 - x - 0.12 = 0 \]**Tasks:**a. Perform 5 iterations with initial guess \( x_0 = 1 \)b. Perform 5 iterations with initial guess \( x_0 = 0.5 \)---This exercise involves solving the given equation using the fixed-point iteration method. The fixed-point iteration is an numerical method for finding an approximation to the root of a real-valued function. With an initial guess \( x_0 \), the iteration proceeds as follows:\[ x_{n+1} = g(x_n) \]where \( g(x) \) is derived from the original equation \( f(x) = 0 \).To apply the fixed-point iteration method for the given equation:\[ x^4 - x - 0.12 = 0 \]we need to re-arrange it into the form \( x = g(x) \). One possible rearrangement might be:\[ x = \sqrt[4]{x + 0.12} \]Then, use this form to perform the iterations as specified.1. **First Initialization \( x_0 = 1 \)** - Perform 5 iterations:\[\begin{align*}x_1 & = g(x_0) \\x_2 & = g(x_1) \\x_3 & = g(x_2) \\x_4 & = g(x_3) \\x_5 & = g(x_4)\end{align*}\]2. **Second Initialization \( x_0 = 0.5 \)** - Perform 5 iterations:\[\begin{align*}x_1 & = g(x_0) \\x_2 & = g(x_1) \\x_3 & = g(x_2) \\x_4 & = g(x_3) \\x_5 & = g(x_4)\end{align*}\]This iterative process is used to approximate a solution to the equation. The results of the iterations will show how the approximations evolve towards the actual root of the equation with different initial guesses.

Name: Analysis and Methods Clear writing, please ? **Fixed-Point Iteration E
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Description: Analysis and Methods Clear writing, please ? **Fixed-Point Iteration Exercise****Problem Statement:**1. Solve by fixed-point iteration:\[ x^4 - x - 0.12 = 0 \]**Tasks:**a. Perform 5 iterations with initial guess \( x_0 = 1 \)b. Perform 5 iterations w

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Answered: 1. Solve by fixed-point iteration: x* –…

Math

Advanced Math

1. Solve by fixed-point iteration: x* – x – 0.12 = 0 a. Do 5 iterations with xo = 1 b. Do 5 iterations with x, = 0.5

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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