Bounding Zolotarev Numbers Using Faber Rational Functions

被引：0
作者：
Daniel Rubin
Alex Townsend
Heather Wilber
机构：
[1] Cornell University,Mathematics Department
[2] Cornell University,Center for Applied Mathematics
来源：
Constructive Approximation | 2022年 / 56卷
关键词：
Faber rational functions; Zolotarev; Conformal maps; Singular values; Rational approximation; 26C15; 30C20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
By closely following a construction by Ganelius, we use Faber rational functions to derive tight explicit bounds on Zolotarev numbers. We use our results to bound the singular values of matrices, including complex-valued Cauchy matrices and Vandermonde matrices with nodes inside the unit disk. We construct Faber rational functions using doubly connected conformal maps and use their zeros and poles to supply shift parameters in the alternating direction implicit method.
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页码：207 / 232
页数：25
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