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 Inverse Iteration Xorter Fellow   Posts: 93 Threads: 30 Joined: Aug 2016 02/04/2019, 10:27 PM (01/02/2019, 10:04 PM)MrFrety Wrote: > What is the inverse method of iteration?                 The closest thing I've found is counting iterations of the inverse. As an algorithm:      Start with the outcome of your iteration of a group element as input. Count how often you can apply the corresponding inverse group element until you reach the neutral element. The counted number gives you the original number N of iterations. Let me use another notation for iteration as iterative multiplication: a ( O Z 0 ) b = a O b a ( O Z 1 ) b = a O a O ... O a, b times which is the first iteration of operator O a ( O Z n ) b = a ( O Z n-1 ) a ( O Z n-1 ) ... ( O Z n-1 ) a, b times So a ( + Z n-1 ) b = a [n] b which is the well-known n-ation, like tetration (n=4). It is binary operator, it needs an operator (e.g. addition, composition, logical and) and a number which is the level of the iteration. So it has two inverses: 1st is a trivial uniteration: ( O Z n ) Z -n = O 2nd is the iterative logarithm you talked about. It is a good method to get the inverse of the operator O, and apply it times such you do not get the neutral element... but what if you fall through the neutral element like how at function gamma. Let us define gamma as a binary operator: gamma_b(b,x) = int from 0 to +oo b^t/t^x dt. As I see this operator is between the exponentiation and tetration because of the limits of these quationts. If I sign iterative logarithm as the following: Zlog(O) - Zlog(P) = n, so that P Z n = O, then what is Zlog(gamma_b)? Xorter Unizo « Next Oldest | Next Newest »

 Messages In This Thread Inverse Iteration - by Xorter - 09/18/2016, 10:36 AM RE: Inverse Iteration - by MrFrety - 01/02/2019, 10:04 PM RE: Inverse Iteration - by Xorter - 02/04/2019, 10:27 PM RE: Inverse Iteration - by MrFrety - 02/05/2019, 09:58 AM

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