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.
In this study, we propose a new approach for development of absorbing boundary conditions for scalar-wave propagation problems in infinite media based on a root-finding algorithm for the solution of the exact wave dis...
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In this study, we propose a new approach for development of absorbing boundary conditions for scalar-wave propagation problems in infinite media based on a root-finding algorithm for the solution of the exact wave dispersion relation. We select the Newton-Raphson method as the root-finding algorithm in the present study and assess the accuracy of the newly developed boundary condition by estimating its reflection coefficient. Furthermore, we evaluate and verify the stability of the boundary condition. We apply our development to various scalar-wave propagation problems and demonstrate that the proposed approach leads to accurate and stable computations (C) 2017 Elsevier B.V. All rights reserved.
The performance of photovoltaic models depends significantly on the accuracy of their parameters, which are determined by the chosen method and objective function. Extracting these parameters accurately under differen...
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The performance of photovoltaic models depends significantly on the accuracy of their parameters, which are determined by the chosen method and objective function. Extracting these parameters accurately under different environmental conditions is essential to enhance reliability, accuracy, and minimize system costs. In this research, a novel technique is proposed for extracting the electrical parameters of the solar cell single diode model, including saturation current, serial resistance, parallel resistance, and ideality factor. To overcome the challenges posed by the chaotic behavior of the I-V curve equation, an improved Iterative root-finding algorithm is introduced. This algorithm acts as an optimization tool, increasing the likelihood of obtaining highly accurate solutions by minimizing the quadratic error between experimental and theoretical characteristics in a shorter time frame. The numerical and experimental results demonstrate the effectiveness of this approach in solar module modeling, showing squared errors approaching zero. This study opens new possibilities for improving the accuracy and reliability of photovoltaic models, leading to more efficient solar energy systems.
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.
Minimizing finite sums of smooth and strongly convex functions is an important task in machine learning. Recent work has developed stochastic gradient methods that optimize these sums with less computation than method...
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Minimizing finite sums of smooth and strongly convex functions is an important task in machine learning. Recent work has developed stochastic gradient methods that optimize these sums with less computation than methods that do not exploit the finite sum structure. This speedup results from using efficiently constructed stochastic gradient estimators, which have variance that diminishes as the algorithm progresses. In this work, we ask whether the benefits of variance reduction extend to fixed point and root-finding problems involving sums of nonlinear operators. Our main result shows that variance reduction offers a similar speedup when applied to a broad class of root-finding problems. We illustrate the result on three tasks involving sums of n nonlinear operators: averaged fixed point, monotone inclusions, and nonsmooth common minimizer problems. In certain "poorly conditioned regimes," the proposed method offers an n-fold speedup over standard methods.
In this paper we propose a variation of the Ehrlich-Aberth method for the simultaneous refinement of the zeros of H-palindromic polynomials. (C) 2013 Elsevier B.V. All rights reserved.
In this paper we propose a variation of the Ehrlich-Aberth method for the simultaneous refinement of the zeros of H-palindromic polynomials. (C) 2013 Elsevier B.V. All rights reserved.
A detailed method for determining the dielectric constant of materials using a Ka-band free-space transmission/reflection measurement system is presented. Since the measurement system was designed to minimise the over...
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A detailed method for determining the dielectric constant of materials using a Ka-band free-space transmission/reflection measurement system is presented. Since the measurement system was designed to minimise the overall cost of the system, correction terms and a smoothing process were necessary to account for limitations in the hardware. The different steps involved in the determination process are explained and their effect on the S-parameters is presented. A through-reflect-match (TRM) free-space calibration method was used, which greatly reduces system errors owing to its simple and stationary nature. The dynamic range of the measurement system after TRM calibration appeared to be better than 50 dB for the reflection coefficient and 29 dB for the transmission coefficient. To determine the unknown dielectric constant of the material, two numerical extraction techniques, a root-finding algorithm and a genetic algorithm were used. Dielectric constant results for a commercially available microwave substrate material sample are presented for both extraction techniques. The difference between the two extraction techniques was < 1%. Comparison of the dielectric constant value with measurement performed by a standards testing organisation revealed an agreement within 2%.
The content of this paper is twofold. First, it aims to provide some new Newton-like methods for solving the root-finding problem in the complex plane. Moreover a convergence test for the resulted methods is phrased a...
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The content of this paper is twofold. First, it aims to provide some new Newton-like methods for solving the root-finding problem in the complex plane. Moreover a convergence test for the resulted methods is phrased and proved. The pseudo-Newton method of Kalantari for finding the maximum modulus of complex polynomials arises as particular case of the newly proposed procedures. Secondly, a recently introduced Thakur iterative process is used in connection with the newly described methods. Its stability and data dependence is subject to analysis. Ultimately, an illustrative analysis regarding some modified Thakur iteration procedures, is obtained via polynomiographic techniques.
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.
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.
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