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Fast Fourier Analysis for SL2 over a Finite Field and
Fast Fourier Analysis for SL2 over a Finite Field and

... group SL2 (Fq ), where Fq is the finite field of elements. Direct computation of a complete set of Fourier transforms for a complex-valued function on SL2 (Fq ) requires 6 operations. A similar bound holds for performing Fourier inversion. Here we show that for both operations this naive upper bound ...
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... structural and sparsity properties, in this paper we are mainly interested in problems that are both large and sparse. This justifies our emphasis on iterative solvers. Direct solvers, however, are still the preferred method in optimization and other areas. Furthermore, direct methods are often used ...
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Non-negative matrix factorization



NMF redirects here. For the bridge convention, see new minor forcing.Non-negative matrix factorization (NMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.NMF finds applications in such fields as computer vision, document clustering, chemometrics, audio signal processing and recommender systems.
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