On converting numbers to the double-base number system
Valérie Berthé, Laurent Imbert · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2004
This paper is an attempt to bring some theory on the top of some previously unproved experimental statements about the double-base number system (DBNS). We use results from diophantine approximation to address the problem of converting integers into DBNS. Although the material presented in this article is mainly theoretical, the proposed algorithm could lead to very efficient implementations.