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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...
Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation
Detection and construction of an elliptic solution complex cubic-quintic Ginzburg-Landau equation Exactly Solvable and Integrable Systems
2012/4/26
In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example ...
Alternative construction of the closed form of the Green's function for the wavized Maxwell fish-eye problem
Maxwell’s fish-eye problem Green’s function scalar wave optics gradient-index (GRIN) optics
2011/8/31
Abstract: In the recent paper [J.\ Phys.\ A 44 (2011) 065203], we have arrived at the closed-form expression for the Green's function for the partial differential operator describing propagation of a ...
Algorithms for Del Pezzo Surfaces of Degree 5 (Construction, Parametrization)
Algorithms Del Pezzo Surfaces of Degree 5
2010/12/9
It is well known that every Del Pezzo surface of degree 5 defined over k is parametrizable over k. In this paper we give an efficient construction for parametrizing, as well as algorithms for construc...