期刊文献+
共找到10篇文章
< 1 >
每页显示 20 50 100
ON SIMULTANEOUS APPROXIMATION BY LAGRANGE INTERPOLATING POLYNOMIALS 被引量:1
1
作者 T. F. Xie S. P. Zhou 《Analysis in Theory and Applications》 1998年第4期89-97,共9页
This paper considers to replace △_m(x)=(1-x^2)~2(1/2)/n +1/n^2 in the following result for simultaneous Lagrange interpolating approximation with (1-x^2)~2(1/2)/n: Let f∈C_(-1.1)~0 and r=[(q+2)/2],then |f^(k)(x)-P_^... This paper considers to replace △_m(x)=(1-x^2)~2(1/2)/n +1/n^2 in the following result for simultaneous Lagrange interpolating approximation with (1-x^2)~2(1/2)/n: Let f∈C_(-1.1)~0 and r=[(q+2)/2],then |f^(k)(x)-P_^(k)(f,x)|=O(1)△_(n)^(a-k)(x)ω(f^(a),△(x))(‖L_n-‖+‖L_n‖),0≤k≤q, where P_n( f ,x)is the Lagrange interpolating polynomial of degree n+ 2r-1 of f on the nodes X_n U Y_n(see the definition of the text), and thus give a problem raised in [XiZh] a complete answer. 展开更多
关键词 LA APPI ON SIMULTANEOUS APPROXIMATION BY lagrange interpolating polynomialS 卜宁 MATH POI
下载PDF
SIMULTANEOUSE APPROXIMATION TO A DIFFERENTIABLE FUNCTION AND ITS DERIVATIVES BY LAGRANGE INTERPOLATING POLYNOMIALS 被引量:1
2
作者 T.F.Xie S.P.Zhou 《Analysis in Theory and Applications》 1994年第4期100-109,共10页
This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of... This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next). 展开更多
关键词 SIMULTANEOUSE APPROXIMATION TO A DIFFERENTIABLE FUNCTION AND ITS DERIVATIVES BY lagrange interpolating polynomialS APPI ZR
下载PDF
Optimization Methods for Box-Constrained Nonlinear Programming Problems Based on Linear Transformation and Lagrange Interpolating Polynomials
3
作者 Zhi-You Wu Fu-Sheng Bai Jing Tian 《Journal of the Operations Research Society of China》 EI CSCD 2017年第2期193-218,共26页
In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optim... In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optimization methods are developed.The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker(KKT)points in general.Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method.Some numerical examples are reported to show the effectiveness of the proposed methods. 展开更多
关键词 Nonlinear programming Optimality conditions Linear transformation lagrange interpolating polynomials Global optimization method
原文传递
APPROXIMATION PROPERTIES OF LAGRANGE INTERPOLATION POLYNOMIAL BASED ON THE ZEROS OF (1-x^2)cosnarccosx
4
作者 Laiyi Zhu 《Analysis in Theory and Applications》 2006年第2期183-194,共12页
We study some approximation properties of Lagrange interpolation polynomial based on the zeros of (1-x^2)cosnarccosx. By using a decomposition for f(x) ∈ C^τC^τ+1 we obtain an estimate of ‖f(x) -Ln+2(f, ... We study some approximation properties of Lagrange interpolation polynomial based on the zeros of (1-x^2)cosnarccosx. By using a decomposition for f(x) ∈ C^τC^τ+1 we obtain an estimate of ‖f(x) -Ln+2(f, x)‖ which reflects the influence of the position of the x's and ω(f^(r+1),δ)j,j = 0, 1,... , s,on the error of approximation. 展开更多
关键词 lagrange interpolation polynomial zeros of (1 -x^2)cos n arccosx piecewise smooth functions error of approximation
下载PDF
INTERPOLATION WITH LAGRANGE POLYNOMIALS A SIMPLE PROOF OF MARKOV INEQUALITY AND SOME OF ITS GENERALIZATIONS
5
作者 A.Shadrin 《Analysis in Theory and Applications》 1992年第3期51-61,共11页
The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies ... The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies the inequality then for each k=1,n and any x[-1,1]its k-th derivative satisfies the inequality 丨p^(k)(x)丨≤max{丨q^((k))(x)丨,丨1/k(x^2-1)q^(k+1)(x)+xq^((k))(x)丨}. This estimate leads to the Markov inequality for the higher order derivatives of polynomials if we set q=T_n,where Tn is Chebyshev polynomial least deviated from zero. Some other results are established which gives evidence to the conjecture that under the conditions of Theorem 1 the inequality ‖p^((k))‖≤‖q^(k)‖holds. 展开更多
关键词 INTERPOLATION WITH lagrange polynomialS A SIMPLE PROOF OF MARKOV INEQUALITY AND SOME OF ITS GENERALIZATIONS
下载PDF
THE DIVERGENCE OF LAGRANGE INTERPOLATION FOR |x|~a 被引量:2
6
作者 Zhikang Lu Xifang Ge 《Analysis in Theory and Applications》 2005年第4期385-394,共10页
This paper shows that the sequence of Lagrange interpolation polynomials corresponding to the rune tion f(z) =|x|^α(1〈α〈2) on [-1,1] can diverge everywhere in the interval except at zero and the end-points.
关键词 lagrange interpolation polynomial equidistant nodes diverge
下载PDF
ON LAGRANGE INTERPOLATION FOR |X|~α (0 < α < 1) 被引量:1
7
作者 Laiyi Zhu and Zhiyong Huang School of Information People’s University of China Beijing, 100872P. R. China 《Analysis in Theory and Applications》 2009年第1期16-24,共9页
We study the optimal order of approximation for |x|α (0 < α < 1) by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind. It is proved that the Jackson order of approximation is attained.
关键词 lagrange interpolation polynomial Chebyshev nodes Jackson order of ap- proximation
下载PDF
A New Third S.N.Bernstein Interpolation Polynomial
8
作者 何甲兴 李笑牛 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第4期10-16, ,共7页
In this paper,a new third type S.N.Bernstein interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous fun... In this paper,a new third type S.N.Bernstein interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous function f(x) . The convergence order is the best order if \{f(x)∈C j[-1,1],\}0jr, where r is an odd natural number. 展开更多
关键词 uniform approximation the best convergence order lagrange interpolation polynomial
下载PDF
Transportation Problem with Multi-choice Cost and Demand and Stochastic Supply 被引量:2
9
作者 Sankar Kumar Roy 《Journal of the Operations Research Society of China》 EI CSCD 2016年第2期193-204,共12页
This paper analyzes the multi-choice stochastic transportation problem where the cost coefficients of the objective function and the demand parameters of the constraints follow multi-choice parameters.Assume that the ... This paper analyzes the multi-choice stochastic transportation problem where the cost coefficients of the objective function and the demand parameters of the constraints follow multi-choice parameters.Assume that the supply parameters of the constraints in a transportation problem(TP)follow logistic distribution.The main objective of this paper is to select an appropriate choice from the multi-choices for the cost coefficients of the objective function and the demand of the constraints in the TP by introducing Lagrange’s interpolating polynomial in such a way that the total cost is minimized and satisfies the required demand.Using stochastic programming,the stochastic supply constraints of the TP are transformed into deterministic constraints.Finally,a non-linear deterministic model is formulated.Using Lingo software,the optimal solution of the proposed problem is derived.To illustrate the methodology,a real-life problem on the TP is considered. 展开更多
关键词 Transportation problem Multi-choice programming lagrange’s interpolating polynomial Stochastic programming
原文传递
On Ordinary Words of Standard Reed-Solomon Codes over Finite Fields
10
作者 Xiaofan Xu Shaofang Hong 《Algebra Colloquium》 SCIE CSCD 2021年第4期569-580,共12页
Reed-Solomon codes are widely used to establish a reliable channel to transmit information in digital communication which has a strong error correction capability and a variety of efficient decoding algorithm.Usually ... Reed-Solomon codes are widely used to establish a reliable channel to transmit information in digital communication which has a strong error correction capability and a variety of efficient decoding algorithm.Usually we use the maximum likelihood decoding(MLD)algorithm in the decoding process of Reed-Solomon codes.MLD algorithm relies on determining the error distance of received word.Dür,Guruswami,Wan,Li,Hong,Wu,Yue and Zhu et al.got some results on the error distance.For the Reed-Solomon code C,the received word u is called an ordinary word of C if the error distance d(u,C)=n-deg u(x)with u(x)being the Lagrange interpolation polynomial of u.We introduce a new method of studying the ordinary words.In fact,we make use of the result obtained by Y.C.Xu and S.F.Hong on the decomposition of certain polynomials over the finite field to determine all the ordinary words of the standard Reed-Solomon codes over the finite field of q elements.This completely answers an open problem raised by Li and Wan in[On the subset sum problem over finite fields,Finite Fields Appl.14(2008)911-929]. 展开更多
关键词 Reed-Solomon code ordinary word lagrange interpolation polynomial finite field
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部