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

Autor(en): Kunis, Stefan 
Nagel, Dominik
Stichwörter: Colliding nodes; Condition number; Frequency analysis; Mathematics; Mathematics, Applied; PARAMETERS; STABILITY; Super resolution; SUPERRESOLUTION; Vandermonde matrix
Erscheinungsdatum: 2021
Herausgeber: SPRINGER
Journal: NUMERICAL ALGORITHMS
Volumen: 87
Ausgabe: 1
Startseite: 473
Seitenende: 496
Zusammenfassung: 
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.
ISSN: 10171398
DOI: 10.1007/s11075-020-00974-x

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