The Experts below are selected from a list of 18267 Experts worldwide ranked by ideXlab platform
Wang Zhi-guo - One of the best experts on this subject based on the ideXlab platform.
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A VERIFIABLE MULTIPLE SECRETS SHARING SCHEME BASED ON HERMITE Interpolation Polynomial
Journal of Mathematics, 2009Co-Authors: Wang Zhi-guoAbstract:This article studies verifiable secret sharing which is an important research area in information security and cryptography.A new multiple secrets sharing scheme,based on the intractability of the discrete logarithm and two variable one-way function and Hermite Interpolation Polynomial is presented,in which the participants' shadows remain secret and can be reused,and those multiple secrets can be recovered at the same time.
Lu Zhi-kang - One of the best experts on this subject based on the ideXlab platform.
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The Approximation to Function |x|~α by Lagrange Interpolation Polynomials
Journal of Hangzhou Normal University, 2012Co-Authors: Lu Zhi-kangAbstract:The paper studied on the approximation to function |x|α by Interpolation Polynomials,constructed Lagrange Interpolation Polynomial with Chebyshev nodes,obtained the approximation,and proved the approximation coefficient was better than previous results.
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Approximation to function |x|~α by Interpolation Polynomials.
2006Co-Authors: Lu Zhi-kangAbstract:The approximation of |x|~α on by Interpolation Polynomials was considered.It is showed that for n=2m,m∈N,α∈(1,2),F_n(α)C_(α,n)n~α,(lim)n→∞C_(α,n)=π(α+3)+π2~(α-1),where F_(2m)(α)=(max)-1≤x≤1|x|~α-R_(2m)(x),(R_(2m)(x) is) the Lagrange Interpolation Polynomial to |x|~α based on the Chebyshev nodes: x_0=0,x_j=cosj-12π2m(j=1,2,…,n).
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Approximation to function |x|~α by Interpolation Polynomials
Journal of Hangzhou Teachers College, 2005Co-Authors: Lu Zhi-kangAbstract:In the present paper we study the approximation of |x|~α on [-1,1] by Interpolation Polynomials. It is showed that: for n=2m,m∈N,α∈(0,1],F\-n(α)C\-α(n+2)~α,where F(2m)(α)=(max)-1x1||x|~α-Q(2m)(x)|,Q(2m)(x) is the Lagrange Interpolation Polynomial to |x|~α based on the Chebyshev nodes:x\-j=cosjπ2m+1(j=1,2,…,2m+1). This result is better than the previous result.
Meng-fu Wang - One of the best experts on this subject based on the ideXlab platform.
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Precise integration methods based on Lagrange piecewise Interpolation Polynomials
International Journal for Numerical Methods in Engineering, 2009Co-Authors: Meng-fu WangAbstract:This paper introduces two new types of precise integration methods for dynamic response analysis of structures, namely, the integral formula method and the homogenized initial system method. The applied loading vectors in the two algorithms are simulated by the Lagrange piecewise Interpolation Polynomials based on the zeros of the first Chebyshev Polynomial. Developed on the basis of the integral formula and the Lagrange piecewise Interpolation Polynomial and combined with the recurrence relationship of some key parameters in the integral computation suggested in this paper with the solving process of linear algebraic equations, the integral formula method has been set up. On the basis of the Lagrange piecewise Interpolation Polynomial, and transforming the non-homogenous initial system into the homogeneous dynamic system, the homogenized initial system method without dimensional expanding is presented; this homogenized initial system method avoids the matrix inversion operation and is a general homogenized high-precision direct integration scheme. The accuracy of the presented time integration schemes is studied and is compared with those of other commonly used schemes; the presented time integration schemes have arbitrary order of accuracy, wider application and are less time consuming. Two numerical examples are also presented to demonstrate the applicability of these new methods. Copyright © 2008 John Wiley & Sons, Ltd.
Lancelot Pecquet - One of the best experts on this subject based on the ideXlab platform.
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A Hensel Lifting to Replace Factorization in List-Decoding of Algebraic-Geometric and Reed-Solomon Codes
IEEE Transactions on Information Theory, 2000Co-Authors: Daniel Augot, Lancelot PecquetAbstract:This paper presents an algorithmic improvement to Sudan's list-decoding algorithm for Reed-Solomon codes and its generalization to algebraic-geometric codes from Shokrollahi and Wasserman. Instead of completely factoring the Interpolation Polynomial over the function field of the curve, we compute sufficiently many coefficients of a Hensel development to reconstruct the functions that correspond to codewords. We prove that these Hensel developments can be found efficiently using Newton's method. We also describe the algorithm in the special case of Reed-Solomon codes.
Laizhong Song - One of the best experts on this subject based on the ideXlab platform.
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The Chebyshev Interpolation Polynomial algorithm error analysis
2012 IEEE International Conference on Information Science and Technology, 2012Co-Authors: Qiang Cai, Laizhong SongAbstract:Based on the practical and importance of the Chebyshev Interpolation Polynomial algorithm, in order to structure Chebyshev Interpolation Polynomial of high precision possible, having some research on the Chebyshev Interpolation Polynomial algorithm firstly: giving the conditions under the usage of the Chebyshev Interpolation Polynomial and Lagrange Interpolation Polynomial, utilizing numerical simulation experiment to change the equidistant Interpolation by the Lagrange Interpolation Polynomial Interpolation algorithm into the transformation of the not equidistant Interpolation by the Chebyshev Interpolation Polynomial Interpolation algorithm image directly. Secondary, the algorithm error analysis is discussed between the Lagrange Interpolation Polynomial Interpolation and the Chebyshev Interpolation Polynomial Interpolation. Finally, under the case of the number of nodes is equal to or greater than five that the conditions on which the usage of Chebyshev Interpolation Polynomial and Lagrange Interpolation Polynomial are given.
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The Lagrange Interpolation Polynomial algorithm error analysis
2011 International Conference on Computer Science and Service System (CSSS), 2011Co-Authors: Qiang Cai, Laizhong SongAbstract:Based on the Lagrange Interpolation Polynomial algorithm, the error analysis is discussed in this paper. Firstly, we derive the Lagrange Interpolation Polynomial algorithm and introduce the shape function with the usage of related data figures. Secondly, how to derive the Lagrange Interpolation function is also simply introduced. At last, some examples have been given to display the error analysis of the Lagrange Interpolation Polynomial algorithm and two conclusions are suggested to minimize the errors in Lagrange Interpolation.
