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Fast construction of hierarchical matrix representation from matrix–vector multiplication
Fast algorithm Hierarchical matrix construction Randomized singular value decomposition Matrix–vector multiplication Elliptic operator Green’s function
2015/7/14
We develop a hierarchical matrix construction algorithm using matrix–vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses Oelog nT appl...
Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
Removable singularity divergence Hausdorff measure Hausdorff content Radon measure Frostman’s lemma charges strong charges
2012/6/19
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence o...
Vector bundles on elliptic curves and factors of automorphy
elliptic curves factors of automorphy
2010/12/8
We translate the Atiyah’s results on classification of vector bundles on elliptic curves to the language of factors of automorphy.