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Mathematics > Numerical Analysis

arXiv:1812.08645 (math)
[Submitted on 20 Dec 2018 (v1), last revised 21 Oct 2019 (this version, v2)]

Title:On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes

Authors:Stefan Kunis, Dominik Nagel
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Abstract:We prove upper and lower bounds for the spectral condition number of rectangular Vandermonde matrices with nodes on the complex unit circle. The nodes are "off the grid", pairs of nodes nearly collide, and the studied condition number grows linearly with the inverse separation distance. Such growth rates are known in greater generality if all nodes collide or for groups of colliding nodes. For pairs of nodes, we provide reasonable sharp constants that are independent of the number of nodes as long as non-colliding nodes are well-separated.
Comments: 21 pages, 7 figures; minor changes; Remark 4.10 reworked; Remark 3.8, Remark 4.11 and summary added; corrected typos
Subjects: Numerical Analysis (math.NA)
MSC classes: 15A18, 65T40, 42A15
Cite as: arXiv:1812.08645 [math.NA]
  (or arXiv:1812.08645v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1812.08645

Submission history

From: Dominik Nagel [view email]
[v1] Thu, 20 Dec 2018 15:47:25 UTC (743 KB)
[v2] Mon, 21 Oct 2019 18:09:11 UTC (662 KB)
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