Extremum problems for eigenvalues of discrete Laplace operators

Citeable URL: https://ir.library.oregonstate.edu/concern/articles/5m60qs57j

Descriptions

Attribute Name	Values
Creator	Guo, Ren
Abstract	The P1 discretization of the Laplace operator on a triangulated polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the P1 discretization of the Laplace operator. Among all triangles, an equilateral triangle has the maximal first positive eigenvalue. Among all cyclic quadrilateral, a square has the maximal first positive eigenvalue. Among all cyclic n-gons, a regular one has the minimal value of the sum of all positive eigenvalues and the minimal value of the product of all positive eigenvalues. Keywords: extremum, discrete Laplace operator, spectra, cyclic polygon
Resource Type	Article
DOI	https://doi.org/10.1016/j.cagd.2013.02.005
Date Available	2013-07-24T20:58:33+00:00
Date Issued	2013-06
Citation	Guo, R. (2013). Extremum problems for eigenvalues of discrete laplace operators. Computer Aided Geometric Design, 30(5), 451-461. doi:10.1016/j.cagd.2013.02.005
Journal Title	Computer Aided Geometric Design
Journal Volume	30
Journal Issue/Number	5
Academic Affiliation	Mathematics
Rights Statement	Copyright Not Evaluated
Publisher	Elsevier
Peer Reviewed	Yes
Language	English [eng]
Replaces	http://hdl.handle.net/1957/41047