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 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...
متن کاملMonotonicity properties of certain Laplacian eigenvectors
Nath and Paul (Linear Algebra Appl., 460 (2014), 97-110) have shown that the largest distance Laplacian eigenvalue of a path is simple and the corresponding eigenvector has properties similar to the Fiedler vector. We given an alternative proof, establishing a more general result in the process. AMS Classification: 05C05, 05C50
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...
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ژورنال
عنوان ژورنال: Machine Learning
سال: 2010
ISSN: 0885-6125,1573-0565
DOI: 10.1007/s10994-010-5201-z