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 ...
... 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 ...
Numerical solution of saddle point problems
... 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 ...
... 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 ...
Chapter 8 The Log-Euclidean Framework Applied to
... Consequently, the exponential map has a well-defined inverse, the logarithm, log: SPD(n) → S(n). But more is true. It turns out that exp: S(n) → SPD(n) is a diffeomorphism. Since exp is a bijection, the above result follows from the fact that exp is a local diffeomorphism on S(n), because d expS is ...
... Consequently, the exponential map has a well-defined inverse, the logarithm, log: SPD(n) → S(n). But more is true. It turns out that exp: S(n) → SPD(n) is a diffeomorphism. Since exp is a bijection, the above result follows from the fact that exp is a local diffeomorphism on S(n), because d expS is ...
Determinants: Evaluation and Manipulation
... Now you have the tools to solves the following problem, which appeared as Putnam 1999/B5. The highest score on his problem was 2 points by one contestant! By this measure, it is one of the most difficult Putnam problems in history; but knowing the above technique is becomes not so bad. Problem 4 (Pu ...
... Now you have the tools to solves the following problem, which appeared as Putnam 1999/B5. The highest score on his problem was 2 points by one contestant! By this measure, it is one of the most difficult Putnam problems in history; but knowing the above technique is becomes not so bad. Problem 4 (Pu ...
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.