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We introduce a multi-dimensional point-wise multi-domain hybrid Fourier-Continuation/WENO technique (FC-WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and essentially dispersionless, spectral, solution ...
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and sp ...
We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional spatially localized ...
Institute of Electrical and Electronics Engineers2013
A large portion of software is used for numerical calculations in mathematics, physics and engineering applications. Among the things that make verification in this domain difficult is the quantification of numerical errors, such as roundoff errors and err ...
We consider the problem of boolean compressed sensing, which is alternatively known as group testing. The goal is to recover a small number of defective items in a large set from a few collective binary tests. This problem can be formulated as a binary lin ...
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the performance to ...
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the performance to ...
According to a well known theorem of Haussler and Welzl (1987), any range space of bounded VC-dimension admits an epsilon-net of size O (1/epsilon log 1/epsilon). Using probabilistic techniques, Pach and Woeginger (1990) showed that there exist range space ...
Acm Order Department, P O Box 64145, Baltimore, Md 21264 Usa2011
It is an old problem of Danzer and Rogers to decide whether it is possible arrange O(1/epsilon) points in the unit square so that every rectangle of area epsilon contains at least one of them. We show that the answer to this question is in the negative if ...
A large portion of software is used for numerical computation in mathematics, physics and engineering. Among the aspects that make verification in this domain difficult is the need to quantify numerical errors, such as roundoff errors and errors due to the ...
