Loading...
Please wait, while we are loading the content...
Similar Documents
The path resistance method for bounding the smallest nontrivial eigenvalue of a laplacian
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Miller, Gary L. Guattery, Stephen Leighton, Tom |
| Copyright Year | 1997 |
| Description | We introduce the path resistance method for lower bounds on the smallest nontrivial eigenvalue of the Laplacian matrix of a graph. The method is based on viewing the graph in terms of electrical circuits; it uses clique embeddings to produce lower bounds on lambda(sub 2) and star embeddings to produce lower bounds on the smallest Rayleigh quotient when there is a zero Dirichlet boundary condition. The method assigns priorities to the paths in the embedding; we show that, for an unweighted tree T, using uniform priorities for a clique embedding produces a lower bound on lambda(sub 2) that is off by at most an 0(log diameter(T)) factor. We show that the best bounds this method can produce for clique embeddings are the same as for a related method that uses clique embeddings and edge lengths to produce bounds. |
| File Size | 1030926 |
| Page Count | 18 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19970037770 |
| Archival Resource Key | ark:/13960/t72v7gj4h |
| Language | English |
| Publisher Date | 1997-10-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Boundary Value Problems Eigenvalues Laplace Equation Embedding Dirichlet Problem Boundary Conditions Eigenvectors Laplace Transformation Graph Theory Trees Mathematics Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
