x = g(x) Iteration (Edexcel A-Level Mathematics): Flashcards

Choose a suitable start value for $x$.

Find $y$ on the curve using the chosen $x$-value.

Move over to the $y = x$ curve, reuse this $x$-value.

Stop when suitably close to a root is reached.

$x_{n+1} = (3 - x_n^3) / 4$.

A change of sign in the interval function values.

Use Newton-Raphson or bisection methods for roots.

$x_{n+1} = \ln(x_n + 3) / \ln(3)$.

They indicate convergence positions on $x$-axis.

$x_3 \approx 0.66$ (to 2 decimal places).