Pith. sign in

REVIEW 2 cited by

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1812.08645 v2 pith:EHAZFAIN submitted 2018-12-20 math.NA cs.NA

Stefan Kunis , Dominik Nagel This is my paper · ORCID
classification math.NAcs.NA
keywords nodesnumberconditionpairscollidematricesvandermondebounds
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Selecting Optimal Sampling Rate for Stable Super-Resolution

    math.NA 2025-02 reject novelty 6.0 of 10

    A singular-value criterion for choosing the decimation rate in spike-train super-resolution is proposed, but the central proof is invalid.

  2. The spectral properties of Vandermonde matrices with clustered nodes

    math.NA 2019-09 conditional novelty 6.0 of 10

    Clustered Vandermonde column subspaces are nearly orthogonal, so the full singular spectrum reduces to per-cluster analysis and conditioning depends only on local cluster multiplicity.

Pith tools