论文标题
通过LLL算法
Quasiperiodic patterns of the complex dimensions of nonlattice self-similar strings, via the LLL algorithm
论文作者
论文摘要
M. L. lapidus和M. van Frankenhuijsen的晶格字符串近似算法（或LSA算法）是一种通过lattice lattice sibal-sibal-sy-sibal-selimial Fractal string的复数尺寸来近似于非层次自相似分形字符串的复数尺寸。此过程的含义是非ltatice string的复杂维度集具有准膜模式。使用LSA算法，以及由D. A. Bini，G。Fiorentino和L. Robol引起的多项式多项式求解器Mpsold，我们给出了非层次自动效果型曲线的复杂尺寸集合的Quasiperiodic模式的新的，更明显的呈现。该算法的实现需要一种实用方法来生成同时进行双苯胺近似值，在某些情况下，我们可以通过持续分数过程来实现。否则，正如Lapidus和Van Frankenhuijsen所建议的那样，我们使用A. K. Lenstra，H。W。Lenstra和L.Lovász的LLL算法。
The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a lattice self-similar fractal string. The implication of this procedure is that the set of complex dimensions of a nonlattice string has a quasiperiodic pattern. Using the LSA algorithm, together with the multiprecision polynomial solver MPSolve which is due to D. A. Bini, G. Fiorentino and L. Robol, we give a new and significantly more powerful presentation of the quasiperiodic patterns of the sets of complex dimensions of nonlattice self-similar fractal strings. The implementation of this algorithm requires a practical method for generating simultaneous Diophantine approximations, which in some cases we can accomplish by the continued fraction process. Otherwise, as was suggested by Lapidus and van Frankenhuijsen, we use the LLL algorithm of A. K. Lenstra, H. W. Lenstra, and L. Lovász.
