TY - GEN A1 - Henk, Martin A1 - Weismantel, Robert T1 - Hilbert bases of cones related to simultaneous Diophantine approximations and linear Diophantine equations N2 - This paper investigates properties of the minimal integral solutions of a linear diophantine equation. We present best possible inequalities that must be satisfied by these elements which improves on former results. We also show that the elements of the minimal Hilbert basis of the dual cone of all minimal integral solutions of a linear diophantine equation yield best approximations of a rational vector ``from above''. Relations between these cones are applied to the knapsack problem. T3 - ZIB-Report - SC-97-29 Y1 - 1997 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/298 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-2989 ER -