Interlacing families III: Sharper restricted invertibility estimates
Interlacing families III: Sharper restricted invertibility estimates
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交错族 III：更严格的限制可逆性估计
DOI：
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发表时间：
2017
影响因子：
1
通讯作者：
N. Srivastava
中科院分区：
文献类型：
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作者：
A. Marcus;D. Spielman;N. Srivastava
本文利用多项式族的交错法，给出了布尔甘和查夫里有限可逆性原理的一个简单证明，并从两个方面对结果进行了锐化。我们证明了稳定秩可以被Schatten 4范数稳定秩所取代，并且当所考虑的矩阵中的列数不会大大超过其行数时，更紧的界保持不变。我们的界限是由雅可比多项式和相关的拉盖尔多项式的最小零点的分析得出的。
We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri’s Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by the Schatten 4-norm stable rank and that tighter bounds hold when the number of columns in the matrix under consideration does not greatly exceed its number of rows. Our bounds are derived from an analysis of the smallest zeros of Jacobi and associated Laguerre polynomials.