Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Approximation method for super square root
(03/23/2010, 10:54 AM)bo198214 Wrote: To compute the inverse function of a strictly increasing function a method that always works is bisection.
perhaps you start with an integer number as you described.
Then you know the real value such that must lie in the interval , set .
Next you divide the interval into two halfes by , and you know that must either be in the left half or in the right half ; in the first case must and in the second case . You choose the new interval accordingly.
And do again bisection on it.
By repetition of bisection you can compute the to arbitrary precision (in the above argumentation I assumed that the solution is never on the boundary of the interval, in which case one can abort the bisection, having found the solution).

For a more concise description see wikipedia.
There are also other root-finding algortithms, like Newton method, etc.

Yeah it's not the most accurate method, but it's done in one step without repetition or recursion, so it would be good more mental math enthusiasts.

Messages In This Thread
RE: Approximation method for super square root - by Ztolk - 03/23/2010, 02:33 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  My interpolation method [2020] tommy1729 1 422 02/20/2020, 08:40 PM
Last Post: tommy1729
  Kneser method question tommy1729 9 1,806 02/11/2020, 01:26 AM
Last Post: sheldonison
  Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 679 09/09/2019, 10:55 PM
Last Post: tommy1729
  Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 976 09/09/2019, 10:50 PM
Last Post: tommy1729
  Is bugs or features for super-logarithm? Ember Edison 10 4,580 08/07/2019, 02:44 AM
Last Post: Ember Edison
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 7,729 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 5,274 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Inverse super-composition Xorter 11 14,902 05/26/2018, 12:00 AM
Last Post: Xorter
  The super 0th root and a new rule of tetration? Xorter 4 4,775 11/29/2017, 11:53 AM
Last Post: Xorter
  The tangent approximation sheldonison 0 1,511 02/11/2017, 11:36 PM
Last Post: sheldonison

Users browsing this thread: 1 Guest(s)