Steffensen's method: Difference between revisions
→The problem we wish to solve
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Line 81:
fun y_convex_left_parabola (t : double) : double =
de_casteljau (1.0, 2.0, 3.0, t)
Plugging <math>x(t)</math> and <math>y(t)</math> into the implicit equation, and writing <math>f(t)</math> as the function whose fixed points are to be found:
fun implicit_equation (x : double, y : double) : double =
(5.0 * x * x) + y - 5.0
fun f (t : double) : double = (* find fixed points of this function *)
let
val x = x_convex_left_parabola (t)
val y = y_convex_left_parabola (t)
in
implicit_equation (x, y) + t
end
What is left to be done is simple, but tricky: use the <code>steffensen_aitken</code> function to find those fixed points.
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