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
In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate ...In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.展开更多
This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by...This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by this thought, we convert the equations into the associated algebraic equations. The results of the numerical examples are given to illustrate that the approximated method is feasible and efficient.展开更多
We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algo...We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.展开更多
In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis...In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis function sets of these polynomialinterpolation methods are given. An example also shows the effectiveness of the results.展开更多
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.
文摘In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.
文摘This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by this thought, we convert the equations into the associated algebraic equations. The results of the numerical examples are given to illustrate that the approximated method is feasible and efficient.
基金This paper is a talk on the held in Nanjing, P. R. China, July, 2004.
文摘We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.
文摘In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis function sets of these polynomialinterpolation methods are given. An example also shows the effectiveness of the results.
