An algorithm based on the Ehrlich-Aberth root-finding method is presented for the computation of the eigenvalues of a T-palindromic matrix polynomial. A structured linearization of the polynomial represented in the Di...
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An algorithm based on the Ehrlich-Aberth root-finding method is presented for the computation of the eigenvalues of a T-palindromic matrix polynomial. A structured linearization of the polynomial represented in the Dickson basis is introduced in order to exploit the symmetry of the roots by halving the total number of the required approximations. The rank structure properties of the linearization allow the design of a fast and numerically robust implementation of the root-finding iteration. Numerical experiments that confirm the effectiveness and the robustness of the approach are provided. (C) 2011 Elsevier Inc. All rights reserved.
An algorithm based on the Ehrlich-Aberth root-finding method is presented for the computation of the eigenvalues of a T-palindromic matrix polynomial. A structured linearization of the polynomial represented in the Di...
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An algorithm based on the Ehrlich-Aberth root-finding method is presented for the computation of the eigenvalues of a T-palindromic matrix polynomial. A structured linearization of the polynomial represented in the Dickson basis is introduced in order to exploit the symmetry of the roots by halving the total number of the required approximations. The rank structure properties of the linearization allow the design of a fast and numerically robust implementation of the root-finding iteration. Numerical experiments that confirm the effectiveness and the robustness of the approach are provided. (C) 2011 Elsevier Inc. All rights reserved.
It is proved that among the rational iterations locally converging with order s > 1 to the sign function, the Fade iterations and their reciprocals are the unique with the lowest sum of the degrees of numerator and...
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It is proved that among the rational iterations locally converging with order s > 1 to the sign function, the Fade iterations and their reciprocals are the unique with the lowest sum of the degrees of numerator and denominator. (C) 2011 Elsevier Inc. All rights reserved.
Gait is another potential human biometrics to look into whenever face recognition fails in video-based systems as is the case with siblings that have similar faces. We perform analyses on 10 pairs of siblings where th...
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ISBN:
(纸本)9783642254611
Gait is another potential human biometrics to look into whenever face recognition fails in video-based systems as is the case with siblings that have similar faces. We perform analyses on 10 pairs of siblings where their faces are assumed to have similarities. Our gait features are the angular displacement trajectories of walking individuals. We apply smoothing with the Bezier polynomial in our root-finding algorithm for accurate gait cycle extraction. Then, we apply classification using two different classifiers;the linear discriminant analysis (LDA) and the k-nearest neighbour (kNN). The best average correct classification rate (CCR) is 100% with a city-block distance kNN classifier. Hence, it is suggested that in the case where face recognition fails, gait may be the better alternative for biometric identification.
In this paper, we first establish a rational iteration method which can be used as a root-finding algorithm for almost every polynomial. It has no nonrepelling extraneous fixed point in the complex plane and is genera...
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In this paper, we first establish a rational iteration method which can be used as a root-finding algorithm for almost every polynomial. It has no nonrepelling extraneous fixed point in the complex plane and is generally convergent for both quadratic and cubic polynomials. Then some properties of this algorithm are given. By the aid of computer, we produce pictures of the Julia sets for the iterations of some polynomials. Numerical results show that it is a root-finding method with convergence order the same as Halley's method.
Let F-q [X-1,..., X-m] denote the set of polynomials over F-q in m variables, and F-q[X-1,..., X-m]less than or equal to(u) denote the subset that consists of the polynomials of total degree at most u. Let H(T) be a n...
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Let F-q [X-1,..., X-m] denote the set of polynomials over F-q in m variables, and F-q[X-1,..., X-m]less than or equal to(u) denote the subset that consists of the polynomials of total degree at most u. Let H(T) be a nontrivial polynomial in T with coefficients in F-q[X-1,...,X-m]. A crucial step in interpolation-based list decoding of q-ary Reed-Muller (RM) codes is finding the roots of H(T) in F-q[X-1,...,X-m]less than or equal to(u). In this correspondence, we present an efficient root-finding algorithm, which finds all the roots of H(T) in F-q[X-1,..., X-m]less than or equal to(u) The algorithm can be used to speed up the list decoding of RM codes.
A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance t from the received vector, where t can be greater than the error-correction bound. In ...
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A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance t from the received vector, where t can be greater than the error-correction bound. In [18], a list-decoding procedure for Reed-Solomon codes [19] was generalized to algebraic-geometric codes. A recent work [8] gives improved list decodings for Reed-Solomon codes and algebraic-geometric codes that work for all rates and have many applications. However, these list-decoding algorithms are rather complicated. In [17], Roth and Ruckenstein proposed an efficient implementation of the list decoding of Reed-Solomon codes. In this correspondence, extending Roth and Ruckenstein's fast algorithm for findingroots of univariate polynomials over polynomial rings, i.e., the Reconstruct algorithm, we will present an efficient algorithm for finding the roots of univariate polynomials over function fields. Based on the extended algorithm, we give an efficient list-decoding algorithm for algebraic-geometric codes.
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