Posted on 03/17/2015 6:47:36 PM PDT by FlJoePa
In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic multigrid method in the geometric setting for elliptic eigenvalue problems and show its uniform convergence under certain assumptions. Numerical tests are presented for computing the Fiedler vector of several practical graphs, and numerical results show the efficiency and optimality of our proposed cascadic multigrid algorithm.
My Differential Equations class eons ago barely touched on Eigenvalue problems, and I was beyond pissed that they waited to go over Laplace Transforms until I already was forced to learn them because I needed them in my Mechanical Engineering classes.
I was under the impression that the veracis discombubulator took care of that at about 1/2 the price...???
With a brain like that why is he risking concussions playing football?
Maybe his calculus is that he plays 2-3 years saves a few millions and then solves math problems for the rest of his life.
My ode professor Dr. Haw, made sure we covered Laplace Transforms. It sure came in handy when I took control theory. The abstract of this paper is too vague for me to understand. It appears that the author is working on a problem in spectral graph theory, but I could be wrong. A quicker partitioning algorithm would have a lot of practical uses.
>> It was such an unusual post
Indeed, the eigenpost — rarely seen, but satifies forum boundaries.
Interesting stuff thanks for posting.
Thanks for the link. Interesting guy - it would be great if he became a role model for black kids.
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