In this paper, we present a fast algorithm of the complexity O(n log n) for solving the linear systems with coefficient matrix of the Pascal type, which is faster than the algorithm of the complexity O(n(2)) given in ...
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In this paper, we present a fast algorithm of the complexity O(n log n) for solving the linear systems with coefficient matrix of the Pascal type, which is faster than the algorithm of the complexity O(n(2)) given in the paper [M.E.A. El-Mikkawy, On solving linear systems of the Pascal type. Applied mathematics and computation 136 (2003) 195-2021. An application in solving non-homogeneous differential equation with constant coefficients is given. (c) 2005 Elsevier Inc. All rights reserved.
In the present paper we Use the displacement structure approach to introduce a new class of what are called confluent polynomial Vandermonde-like matrices, which generalize the ordinary simple nodes polynomial Vanderm...
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In the present paper we Use the displacement structure approach to introduce a new class of what are called confluent polynomial Vandermonde-like matrices, which generalize the ordinary simple nodes polynomial Vandermonde matrices studied earlier by different authors. The displacement structure approach leads to the explicit inversion formulas for confluent polynomial Vandermonde-like matrices and fast algorithms for inversion and for solving the associated linear systems. (C) 2003 Published by Elsevier Inc.
Ultra-wideband pulse radars are promising candidates for 3-dimensional environment measurements by autonomous robots. Estimating 3-dimensional target shapes by scanning with an omni-directional antenna is an ill-posed...
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Ultra-wideband pulse radars are promising candidates for 3-dimensional environment measurements by autonomous robots. Estimating 3-dimensional target shapes by scanning with an omni-directional antenna is an ill-posed inverse problem. Conventional algorithms such as the synthetic aperture method or parametric algorithms have a problem in terms of their calculation times. We have clarified the existence of a reversible transform between received data and target shapes for 3-dimensional systems. Calculation times are remarkably reduced by applying this transform because it directly estimates target shapes without iterations. We propose a new algorithm based on the transform and present an application example using numerical simulations. We confirm that the proposed algorithm has sufficient accuracy and a short calculation time.
In this paper, we derive an L1 Legendre-Galerkin spectral method with fast algorithm based on an efficient sum-of-exponentials (SOE) approximation for the kernel t(-1-alpha) to solve the two-dimensional nonlinear coup...
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In this paper, we derive an L1 Legendre-Galerkin spectral method with fast algorithm based on an efficient sum-of-exponentials (SOE) approximation for the kernel t(-1-alpha) to solve the two-dimensional nonlinear coupled time fractional Schrodinger equations. The numerical method is stable without the Courant-Friedrichs-Lewy (CFL) conditions based on the error splitting argument technique and the discrete fractional Gronwall type inequality. At the same time, we use the fully implicit method to deal with the nonlinear terms. For the non-smooth solution, we employ the graded mesh method. Moreover, we estimate the parameters including fractional derivative index and the coefficients of the nonlinear term in the equations by applying the Cuckoo Search algorithm related to Levy flights. Numerical examples are given to verify the theoretical analysis and confirm the effectiveness of the fast algorithm and the estimation method. (C) 2020 Elsevier Ltd. All rights reserved.
algorithms for expansion over spherical harmonics are often used in electrostatic held calculation, calculation of the density functions in quantum chemistry and calculation of molecular surfaces. It usually includes ...
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algorithms for expansion over spherical harmonics are often used in electrostatic held calculation, calculation of the density functions in quantum chemistry and calculation of molecular surfaces. It usually includes expansion over spherical harmonics of degrees to several dozens. The usual method is to use an integration method over some grid on the unit sphere and in fact is a multiplication of the matrix of values of spherical harmonics in the grid points by a vector of values of the expanding function in the set of points. This algorithm executes O(NL(2)) operations where N is the number of the grid points and L is the maximal degree of the spherical harmonics involved. We provide an algorithm of complexity O(NLlog(2) L) for multiplication of the matrix of values of spherical harmonics in points of an arbitrary grid on the unit sphere. The algorithm is based on interrelation between spherical harmonics and Legendre polynomials and on a fast algorithm for expansion over Legendre polynomials.
In this paper, we analyze a novel algorithm for 2-D ARMA model parameter estimation in the presence of noise and then develop a fast and efficient blind image restoration algorithm. We show that the novel algorithm ca...
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In this paper, we analyze a novel algorithm for 2-D ARMA model parameter estimation in the presence of noise and then develop a fast and efficient blind image restoration algorithm. We show that the novel algorithm can minimize a quadratic convex optimization problem and has a lower computational complexity than the conventional algorithms. As a result, the novel algorithm involves no convergence and local minimum issue. Moreover, the proposed blind image restoration algorithm can overcome the local minimization problem. Computed results confirm that the novel algorithm can more quickly obtain more accurate estimates than the conventional algorithms in the presence of noise. (C) 2013 Elsevier Ltd. All rights reserved.
In this paper, a generalized fast computational algorithm for the n-dimensional discrete cosine transform (DCT) of length N = 2(m) (m greater than or equal to 2) is presented. The developed algorithm is proved and its...
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In this paper, a generalized fast computational algorithm for the n-dimensional discrete cosine transform (DCT) of length N = 2(m) (m greater than or equal to 2) is presented. The developed algorithm is proved and its efficiency is evaluated theoretically, The theoretical results show that compared with the conventional method of computing the one-dimensional along n directions, the number of multiplications needed by our algorithm is only 1/n of that required by the conventional method;for the total number of additions, the latter is a bit more when N less than or equal to 8 and much fewer when N greater than or equal to 16 than the former. To validate the proposed algorithm, me take the case when n = 3 as an example and apply it to motion-picture coding. The results show that our method is superior to MPEG-2 in speed and coding performance. The algorithm is clearly described and it is easy to make a computer program for implementation.
At present, the research of inductive pulsed power supply (PS) based on the high-temperature superconducting pulsed power transformer (HTSPPT) has many qualitative descriptions, but there is a lack of direct theoretic...
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A fast algorithm is presented for determining the linear complexity and the minimal polynomial of a sequence with period 2p(n) over GF (q), where p and q are odd prime, and q is a primitive root (mod p(2)). The algori...
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A fast algorithm is presented for determining the linear complexity and the minimal polynomial of a sequence with period 2p(n) over GF (q), where p and q are odd prime, and q is a primitive root (mod p(2)). The algorithm uses the fact that in this case the factorization of x(2)p(n) - 1 is especially simple.
A dynamic programming algorithm is developed for maximum-likelihood reconstruction of the set of all ancestral amino acid sequences in a phylogenetic tree. To date, exhaustive algorithms that find the most likely set ...
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A dynamic programming algorithm is developed for maximum-likelihood reconstruction of the set of all ancestral amino acid sequences in a phylogenetic tree. To date, exhaustive algorithms that find the most likely set of ancestral states (joint reconstruction) have running times that scale exponentially with the number of sequences and are thus limited to Very few taxa. The time requirement of our new algorithm scales linearly with the number of sequences and is therefore applicable to practically any number of taxa. A detailed description of the new algorithm and an example of its application to cytochrome b sequences are provided.
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