论文标题
Vandermonde矩阵倒数的最大入口
The Largest Entry in the Inverse of a Vandermonde Matrix
论文作者
论文摘要
我们研究了某些Vandermonde矩阵倒数的最大入口（绝对值）的大小。更确切地说，对于每个真正的$ b> 1 $，让$ m_b（n）$成为$ n \ times n $矩阵$ [b^{i j}] _ {0 \ leq i，j <n} $的最大值的最大值。我们证明存在$ \ lim_ {n \ to +\ infty} m_b（n）$，我们为其提供一些公式。
We investigate the size of the largest entry (in absolute value) in the inverse of certain Vandermonde matrices. More precisely, for every real $b > 1$, let $M_b(n)$ be the maximum of the absolute values of the entries of the inverse of the $n \times n$ matrix $[b^{i j}]_{0 \leq i, j < n}$. We prove that $\lim_{n \to +\infty} M_b(n)$ exists, and we provide some formulas for it.
