منابع مشابه
Laplacian graph eigenvectors
If G is a graph, its Laplacian is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. The main thrust of the present article is to prove several Laplacian eigenvector “principles” which in certain cases can be used to deduce the effect on the spectrum of contracting, adding or deleting edges and/or of coalescing vertices. One application is the construction of ...
متن کاملHow can we naturally order and organize graph Laplacian eigenvectors?
When attempting to develop wavelet transforms for graphs and networks, some researchers have used graph Laplacian eigenvalues and eigenvectors in place of the frequencies and complex exponentials in the Fourier theory for regular lattices in the Euclidean domains. This viewpoint, however, has a fundamental flaw: on a general graph, the Laplacian eigenvalues cannot be interpreted as the frequenc...
متن کاملQuadrangulating a Mesh using Laplacian Eigenvectors
Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing methods. While the majority of work in the past has focused on triangular remeshing, the problem of resampling surfaces with quadrilaterals is at least as important. Quadrilaterals are the preferred primitive in many cases, such as Catmull-Clark subdivision surfaces, fluid dyna...
متن کاملThe other eigenvectors of the Laplacian
We are now going to begin our study of the other eigenvalues and eigenvectors of the Laplacian. I will begin the lecture by showing how much of the theory we established can be preserved. We will then determine the eigenvalues of the hypercube, and begin to see why λ 2 is so important. Recall that we showed that the kth eigenvector of a path graph crosses the origin at most k − 1 times. For exa...
متن کاملEigenvalues and Eigenvectors of the Discrete Laplacian
We derive explicit formulas for the eigenvalues and eigenvectors of the Discrete Laplacian on a rectangular grid for the standard finite difference and finite element methods in 1D, 2D, and 3D. Periodic, Dirichlet, Neumann, and mixed boundary conditions are all considered. We show how the higher dimensional operators can be written as sums of tensor products of one dimensional operators, and th...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1998
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)10080-5