Numerical Method20785 marksNumerical: fixed point iterationFixed point iteration and its convergence
Calculate the real root of the given equation using fixed point iteration correct up to 3 significant figures. 2x3 - 2x = 5.
Calculate the real root of the given equation using fixed point iteration correct up to 3 significant figures. $2x^3 - 2x = 5$. [5]
- Equation: $2x^3 - 2x = 5$, i.e. $f(x) = 2x^3 - 2x - 5 = 0$ - Method: Fixed point iteration - Required accuracy: 3 significant figures No initial guess given; must be determined by root location. Rearrange to $x = g(x)$: $$2x^3 = 5 + 2x \implies x = \left(\frac{5 + 2x}{2}\right)^{1/3} = g(x)$$ C...