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• W3104611862 abstract "In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which the matrices have a group structure and an other in which they have rank-one. As an application of the former case, we present a deterministic algorithm that, given the multiplication table of a finite group of size $n$, it constructs an expanding Cayley graph of logarithmic degree in near-optimal O(n^2 log^3 n) time. For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices, which implies an improved deterministic algorithm for spectral graph sparsification of dense graphs. In addition, we give an elementary connection between spectral sparsification of positive semi-definite matrices and element-wise matrix sparsification. As a consequence, we obtain improved element-wise sparsification algorithms for diagonally dominant-like matrices." @default.
• W3104611862 created "2020-11-23" @default.
• W3104611862 creator A5019949317 @default.
• W3104611862 date "2012-01-01" @default.
• W3104611862 modified "2023-10-16" @default.
• W3104611862 title "A Matrix Hyperbolic Cosine Algorithm and Applications" @default.
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• W3104611862 doi "https://doi.org/10.1007/978-3-642-31594-7_71" @default.
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