On the concept of optimality interval
| Contribuinte(s) |
Universitat Pompeu Fabra. Departament d'Economia i Empresa |
|---|---|
| Data(s) |
15/09/2005
|
| Resumo |
The approximants to regular continued fractions constitute `best approximations' to the numbers they converge to in two ways known as of the first and the second kind.This property of continued fractions provides a solution to Gosper's problem of the batting average: if the batting average of a baseball player is 0.334, what is the minimum number of times he has been at bat? In this paper, we tackle somehow the inverse question: given a rational number P/Q, what is the set of all numbers for which P/Q is a `best approximation' of one or the other kind? We prove that inboth cases these `Optimality Sets' are intervals and we give aprecise description of their endpoints. |
| Identificador | |
| Idioma(s) |
eng |
| Direitos |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons info:eu-repo/semantics/openAccess <a href="http://creativecommons.org/licenses/by-nc-nd/3.0/es/">http://creativecommons.org/licenses/by-nc-nd/3.0/es/</a> |
| Palavras-Chave | #Statistics, Econometrics and Quantitative Methods #diofantine approximations #continued fractions #metric theory |
| Tipo |
info:eu-repo/semantics/workingPaper |
