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Journal of Statistical Physics

, Volume 166, Issue 3–4, pp 1029–1035 | Cite as

On the Spectral Gap of a Square Distance Matrix

  • Xinyu Cheng
  • Dong LiEmail author
  • David Shirokoff
  • Brian Wetton
Article
  • 299 Downloads

Abstract

We consider a square distance matrix which arises from a preconditioned Jacobian matrix for the numerical computation of the Cahn–Hilliard problem. We prove strict negativity of all but one associated eigenvalues. This solves a conjecture in Christieb et al. (J Comput Phys 257:193–215, 2014).

Keywords

Distance matrix Eigenvalue Solvability 

Notes

Acknowledgements

X. Cheng, D. Li and B. Wetton were supported in part by NSERC Discovery grants. This work was supported by a Grant from the Simons Foundation (\(\#359610\), David Shirokoff).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Xinyu Cheng
    • 1
  • Dong Li
    • 1
    Email author
  • David Shirokoff
    • 2
  • Brian Wetton
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA

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