论文标题
具有较大贪婪总和的阈值贪婪算法的性能
Performance of the Thresholding Greedy Algorithm with Larger Greedy Sums
论文作者
论文摘要
本文的目的是研究阈值贪婪算法（TGA）的性能，当我们将贪婪总和的大小增加一个恒定因子$λ\ geqslant 1 $时。我们介绍了所谓的$λ$ - 几乎是贪婪和$λ$的贪婪基地。 $λ= 1 $的情况为我们提供了几乎贪婪和（强）部分贪婪基地的经典定义。我们表明，只有当所有（某些）$λ\ geqslant 1 $的最大贪婪时，基础几乎是贪婪的。但是，对于每个$λ> 1 $，存在一个无条件的基础，即$λ$的贪婪，但不是$ 1 $ - 部分贪婪。此外，我们在基础上调查并举例说明 1。几乎不贪婪，$ 1 $，而是$λ$ - 几乎是贪婪，某些$λ> 1 $，而常数$ 1 $，并且 2。不强烈的部分贪婪，$ 1 $，但$λ$ - 部分是贪婪，对于某些$λ> 1 $而言，$ 1 $ $ 1 $。 最后，我们证明了不同贪婪型基础的各种特征。
The goal of this paper is to study the performance of the Thresholding Greedy Algorithm (TGA) when we increase the size of greedy sums by a constant factor $λ\geqslant 1$. We introduce the so-called $λ$-almost greedy and $λ$-partially greedy bases. The case when $λ= 1$ gives us the classical definitions of almost greedy and (strong) partially greedy bases. We show that a basis is almost greedy if and only if it is $λ$-almost greedy for all (some) $λ\geqslant 1$. However, for each $λ> 1$, there exists an unconditional basis that is $λ$-partially greedy but is not $1$-partially greedy. Furthermore, we investigate and give examples when a basis is 1. not almost greedy with constant $1$ but is $λ$-almost greedy with constant $1$ for some $λ> 1$, and 2. not strong partially greedy with constant $1$ but is $λ$-partially greedy with constant $1$ for some $λ> 1$. Finally, we prove various characterizations of different greedy-type bases.
