On the Spectral Gap of a Square Distance Matrix

Xinyu Cheng; Dong Li; David Shirokoff; Brian Wetton

doi:10.1007/s10955-016-1685-7

On the Spectral Gap of a Square Distance Matrix

Xinyu Cheng, Dong Li, David Shirokoff, Brian Wetton

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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).

Original language	English (US)
Pages (from-to)	1029-1035
Number of pages	7
Journal	Journal of Statistical Physics
Volume	166
Issue number	3-4
DOIs	https://doi.org/10.1007/s10955-016-1685-7
State	Published - Feb 1 2017

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Distance matrix
Eigenvalue
Solvability

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10.1007/s10955-016-1685-7

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title = "On the Spectral Gap of a Square Distance Matrix",

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).",

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AU - Shirokoff, David

AU - Wetton, Brian

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N2 - 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).

AB - 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).

KW - Distance matrix

KW - Eigenvalue

KW - Solvability

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JO - Journal of Statistical Physics

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On the Spectral Gap of a Square Distance Matrix

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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