منابع مشابه
Butterfly Factorization
The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the matrix and its adjoint are available or the entries of the matrix can be sampled individually. For an N ×N matrix, the resulting factorization is a product of O...
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This paper introduces the multidimensional butterfly factorization as a data-sparse representation of multidimensional kernel matrices that satisfy the complementary low-rank property. This factorization approximates such a kernel matrix of size N ×N with a product of O(logN) sparse matrices, each of which contains O(N) nonzero entries. We also propose efficient algorithms for constructing this...
متن کاملInterpolative Butterfly Factorization
This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of these transforms satisfy a complementary low-rank property. A preliminary interpolative butterfly factorization is constructed based on interpolative low-ra...
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Concerns about the potential toxicity of pollen from genetically modified maize on neighbouring butterflies prompted urgent studies, reports Nigel Williams.
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That the flap of a butterfly’s wing might lead to a storm or other event halfway around the globe is a popular image used to introduce chaos theory. But two small lepidopterans appear to have played a major part in the scrapping of plans to build a new nuclear power station on a shingle bank in the south-east of England, which is becoming an increasing focus in the International Year of Biodive...
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ژورنال
عنوان ژورنال: Multiscale Modeling & Simulation
سال: 2015
ISSN: 1540-3459,1540-3467
DOI: 10.1137/15m1007173