Dynamical Systems

[Mos5180d]

Let h(y) =[imath]y^2-1[/imath] and [imath]y_n[/imath] be the sequence generated by the Newton-Raphson scheme for approximating the roots of h (which are clearly −1 and 1): [imath]y_{n+1}= y_n-(y_n^2-1)/2y_n[/imath]

Obtain a formula for [imath]y_n[/imath] in terms of n and [imath]y_0[/imath]

Here is my working but I seem to get back to the same position,



But when I input numbers for y_0, the results do not follow that pattern

 

[blamocur]

At this point I don't know how to solve it, but your expression for [imath]y_2[/imath], or for [imath]y_n[/imath] for that matter, does not look right to me.

 

[BigBeachBanana]

[EDITED] Never mind, you're defining y as the independent variable. Your initial formula is correct.