In this paper, we investigate the negative extremums of fundamental functions of Lagrange interpolation based on Chebyshev nodes. Moreover, we establish some companion results to the theorem of J. Szabados on the posi...In this paper, we investigate the negative extremums of fundamental functions of Lagrange interpolation based on Chebyshev nodes. Moreover, we establish some companion results to the theorem of J. Szabados on the positive extremum.展开更多
In this paper,Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation.First of all,the interpolation basis function is appli...In this paper,Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation.First of all,the interpolation basis function is applied to treat the spatial variables and their partial derivatives,and the collocation method for solving the second order differential equations is established.Secondly,the differential matrix is used to simplify the given differential equations on a given test node.Finally,based on three kinds of test nodes,numerical experiments show that the present scheme can not only calculate the high wave numbers problems,but also calculate the variable wave numbers problems.In addition,the algorithm has the advantages of high calculation accuracy,good numerical stability and less time consuming.展开更多
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.
In this paper, we discuss the average errors of multivariate Lagrange interpolation based on the Chebyshev nodes of the first kind. The average errors of the interpolation sequence are determined on the multivariate W...In this paper, we discuss the average errors of multivariate Lagrange interpolation based on the Chebyshev nodes of the first kind. The average errors of the interpolation sequence are determined on the multivariate Wiener space.展开更多
For the weighted approximation in Lp-norm, we determine the asymptotic order for the p- average errors of Lagrange interpolation sequence based on the Chebyshev nodes on the Wiener space. We also determine its value i...For the weighted approximation in Lp-norm, we determine the asymptotic order for the p- average errors of Lagrange interpolation sequence based on the Chebyshev nodes on the Wiener space. We also determine its value in some special case.展开更多
We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x?a 1), 1/(x?a 2), …}, and both the remainder a...We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x?a 1), 1/(x?a 2), …}, and both the remainder and convergence of the quadrature formula established here are discussed. Our results extend some classical ones.展开更多
According to the precise ephemeris has only provided satellite position that is discrete not any time,so propose that make use of interpolation method to calculate satellite position at any time.The essay take advanta...According to the precise ephemeris has only provided satellite position that is discrete not any time,so propose that make use of interpolation method to calculate satellite position at any time.The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation,Newton interpolation,Hermite interpolation,Cubic spline interpolation method,Chebyshev fitting method respectively,which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method is the worst,the precision of Chebyshev fitting is better than Hermite interpolation method. Lagrange interpolation and Newton interpolation are better than other methods in precision. Newton interpolation method has the advantages of high speed and high precision. Therefore,Newton interpolation method has a certain scientific significance and practical value to get the position of the satellite quickly and accurately.展开更多
文摘In this paper, we investigate the negative extremums of fundamental functions of Lagrange interpolation based on Chebyshev nodes. Moreover, we establish some companion results to the theorem of J. Szabados on the positive extremum.
基金partially supported by National Natural Science Foundation of China(11772165,11961054,11902170)Key Research and Development Program of Ningxia(2018BEE03007)+1 种基金National Natural Science Foundation of Ningxia(2018AAC02003,2020AAC03059)Major Innovation Projects for Building First-class Universities in China’s Western Region(Grant No.ZKZD2017009).
文摘In this paper,Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation.First of all,the interpolation basis function is applied to treat the spatial variables and their partial derivatives,and the collocation method for solving the second order differential equations is established.Secondly,the differential matrix is used to simplify the given differential equations on a given test node.Finally,based on three kinds of test nodes,numerical experiments show that the present scheme can not only calculate the high wave numbers problems,but also calculate the variable wave numbers problems.In addition,the algorithm has the advantages of high calculation accuracy,good numerical stability and less time consuming.
文摘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.
文摘In this paper, we discuss the average errors of multivariate Lagrange interpolation based on the Chebyshev nodes of the first kind. The average errors of the interpolation sequence are determined on the multivariate Wiener space.
基金Supported by National Natural Science Foundation of China(Grant No.10471010)
文摘For the weighted approximation in Lp-norm, we determine the asymptotic order for the p- average errors of Lagrange interpolation sequence based on the Chebyshev nodes on the Wiener space. We also determine its value in some special case.
文摘We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x?a 1), 1/(x?a 2), …}, and both the remainder and convergence of the quadrature formula established here are discussed. Our results extend some classical ones.
基金Supported by the National Natural Science Foundation of China(41474020)
文摘According to the precise ephemeris has only provided satellite position that is discrete not any time,so propose that make use of interpolation method to calculate satellite position at any time.The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation,Newton interpolation,Hermite interpolation,Cubic spline interpolation method,Chebyshev fitting method respectively,which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method is the worst,the precision of Chebyshev fitting is better than Hermite interpolation method. Lagrange interpolation and Newton interpolation are better than other methods in precision. Newton interpolation method has the advantages of high speed and high precision. Therefore,Newton interpolation method has a certain scientific significance and practical value to get the position of the satellite quickly and accurately.