Discrete Nodal Domain Theorems
By E. BrianDavies, G. L. Gladwell, J. Leydold, Peter F. Stadler. 2000
172 citations recorded by the source corpus.
We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem. (author's abstract)
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6513404873191a42990b2d6231d0dee5a10269ee
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Antonio Ortega
- José M. F. Moura
- David I. Shuman
- Pascal Frossard
- Sunil K. Narang
- Jiayu Zhou
- Pierre Vandergheynst
- Jelena Kovacevic
In Geometry and Topology
- José M. F. Moura
- Antonio Ortega
- Fei Wang
- Pierre Vandergheynst
- Pascal Frossard
- Sunil K. Narang
- Jelena Kovacevic
- David I. Shuman
Citations in the corpus
- Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems (2021, methodology): “In this work, the GCN is constructed based on the Chebyshev spectral graph convolution operator [41], which is derived from the spectral convolution theorem [42], where Chebyshev polynomials are introduced to avoid expensive eigen-decomposition.”
- A Multiscale Pyramid Transform for Graph Signals (2013, background): “…from two different perspectives - first from a more intuitive view as a generalization of downsampling techniques for special types of graphs, and then from a more theoretical point of view by connecting the vertex selection problem to graph coloring, spectral clustering, and nodal domain theory.”
- Perfect Reconstruction Two-Channel Wavelet Filter Banks for Graph Structured Data (2011, background): “These results are related to ‘nodal domain theorems’ and readers are directed to [16] for more details.”
- Graph convolutional networks for computational drug development and discovery (2019, background): “The spectral convolution theorem [26] pursues Fourier-like basis for signals defined on graph, typically focus on the properties of graph Laplacian matrix L .”
- Graph Signal Processing: Overview, Challenges, and Applications (2017, background): “As the eigenvalue index i increases, the number of oscillations tends to increase as well [86].”
- Courant's Nodal Line Theorem and Its Discrete Counterparts (2002, background): “Thus partition u in the form uT ={ vT 1 , v T 2 ,..., v T m, 0}. ( 14 )”