分胞算法与非齐次Lagrange谱和Markoff谱
The divided cell algorithm and the inhomogeneous Lagrange and Markoff spectra
摘要：
Delone于1947年提出了计算二元二次型非齐次极小值的分胞算法，E. S. Barnes和H. P. F. 1950年代的Swinnerton-Dyer。我们展示了如何在过去五十年的进步，在符号计算和我们的理解均匀的光谱可以结合起来，使划分的细胞更有用的组织信息的非齐次逼近问题。我们分析的一个关键部分依赖于Jane Pitman的工作，他将分裂单元算法与常规连分数算法联系起来。特别地，与连分数的关系允许对同一问题的两个划分的单元进行比较，而不需要步进通过连接它们的划分的单元的链。
英文摘要：
The divided cell algorithm was introduced by Delone in 1947 to calculate the inhomogeneous minima of binary quadratic forms and developed further by E. S. Barnes and H. P. F. Swinnerton-Dyer in the 1950s. We show how advances of the past fifty years in both symbolic computation and our understanding of homogeneous spectra can be combined to make divided cells more useful for organizing information about inhomogeneous approximation problems. A crucial part of our analysis relies on work of Jane Pitman, who related the divided cell algorithm to the regular continued fraction algorithm. In particular, the relation to continued fractions allows two divided cells for the same problem to be compared without stepping through the chain of divided cells connecting them.
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