functional square root; half iterate; iterated function
Computational Methods in Science and Technology, Vol. 24, iss. 3 (2018), s. 187–209
Four algorithms determining all functional square roots (half iterates) and seven algorithms finding one functional
square root of any function f : X ! X defined on a finite set X, if these square roots exist, are presented herein. Time
efficiency of these algorithms depending on the complexity of examined functions is compared and justification of correctness
is given. Moreover, theorems which make finding half iterates possible in some cases or facilitate this task are formulated.