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Your search keyword '"*VECTORS (Calculus)"' showing total 2 results
2 results on '"*VECTORS (Calculus)"'

1. The unsupervised optimum linear finite length filter for fourth order wide sense stationary single output systems.

Author

Jamali, Hamadi

Subjects
*VECTORS (Calculus), *COMPUTER simulation, *WIENER filters (Signal processing), *ALGORITHMS, *COMPUTATIONAL complexity
Abstract

Abstract The finite length absolute minimum vectors of the Constant Modulus (CM) criterion with an arbitrary source and a single output linear regression model are shown to equal the Wiener filter or one of its phase shifted versions. The exact equations for these vectors are also provided and depend on the second and the fourth order statistical moments of the sample sequence only. These expressions describe the behavior of the Constant Modulus Algorithm (CMA) when it operates at the desired global minimum and expose key characteristics of the CM minimization approach. These characteristics include the existence conditions, the persistency of excitation, the computational complexity, the excess CM cost, the robustness to an additive noise, and the tolerance to the length variations. Moreover, several computer simulation experiments are included to validate our findings. [ABSTRACT FROM AUTHOR]

Published
2019
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2. Sparse approximation is provably hard under coherent dictionaries.

Author

Çivril, A.

Subjects
*SPARSE approximations, *NP-hard problems, *ALGORITHMS, *SET theory, *VECTORS (Calculus)
Abstract

It is well known that sparse approximation problem is NP-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the coherence μ of the dictionary represented by an M × N matrix from which a subset of k column vectors is selected. All these results assume μ = O ( k − 1 ) . This article is an attempt to bridge the big gap between the negative result of NP-hardness under general dictionaries and the positive results under this restrictive assumption. In particular, it suggests that the aforementioned assumption might be asymptotically the best one can make to arrive at any efficient algorithmic result under well-known conjectures of complexity theory. In establishing the results, we make use of a new simple multilayered PCP which is tailored to give a matrix with small coherence combined with our reduction. [ABSTRACT FROM AUTHOR]

Published
2017
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