On the Spectral Gap of a Square Distance Matrix
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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).
KeywordsDistance matrix Eigenvalue Solvability
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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