Mathematics – Numerical Analysis
Scientific paper
2005-08-30
SIMAX Volume 29 Issue 1 Pages 15-32, 2006.
Mathematics
Numerical Analysis
Accepted to SIMAX
Scientific paper
10.1137/060649070
Many inequality relations between real vector quantities can be succinctly expressed as ``weak (sub)majorization'' relations. We explain these ideas and apply them in several areas: angles between subspaces, Ritz values, and graph Laplacian spectra, which we show are all surprisingly related... An application of our Ritz values weak majorization result for Laplacian graph spectra comparison is suggested, based on the possibility to interpret eigenvalues of the edge Laplacian of a given graph as Ritz values of the edge Laplacian of the complete graph. We prove that $ \sum_k |\lambda1_k - \lambda2_k| \leq n l,$ where $\lambda1_k$ and $\lambda2_k$ are all ordered elements of the Laplacian spectra of two graphs with the same $n$ vertices and with $l$ equal to the number of differing edges.
Argentati Merico E.
Knyazev Andrew V.
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