A brief interaction with continued fractions
Degree GrantorUniversity of Canterbury
Basic concepts of simple continued fractions are introduced and some important theorems explored. The effect of an infinite continued fraction's elements forming a convergent series is looked at via an example of geometric series. The Gauss-Kuzmin-Wirsing operator, operating on functions on the interval [0, 1], is studied numerically. Its invariant density is explored and the rate at which an initial density transforms into the invariant density shown to be O(e-Sn) for iteration n. The transformation associated with the operator is applied numerically to a single random point in [0, 1] and interpretations of the results given.
SubjectsField of Research::01 - Mathematical Sciences::0104 - Statistics::010406 - Stochastic Analysis and Modelling
- Engineering: Reports