12 citations · 27 across the 13 of their papers we have counts for
13 papers
Barycentric Interpolation Based on Equilibrium Potential
Kelong Zhao, shuhuang Xiang
We present a novel barycentric interpolation algorithm designed for analytic functions defined on the complex plane. The algorithm, which encompasses both poly…
Pointwise error estimates and local superconvergence of Jacobi expansions
Shuhuang Xiang, Desong Kong, Guidong Liu +1
As one myth of polynomial interpolation and quadrature, Trefethen [30] revealed that the Chebyshev interpolation of (with ) at the Clenshaw-Curtis points exhibited…
Eigenvalue Analysis and Applications of the Legendre Dual-Petrov-Galerkin Methods for Initial Value Problems
Desong Kong, Jie Shen, Li-Lian Wang +1
In this paper, we show that the eigenvalues and eigenvectors of the spectral discretisation matrices resulted from the Legendre dual-Petrov-Galerkin (LDPG) method for the th-ord…
Fast linear barycentric rational interpolation for singular functions via scaled transformations
Desong Kong, Shuhuang Xiang
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of sin…
Convergence rates of spectral orthogonal projection approximation for functions of algebraic and logarithmatic regularities
Shuhuang Xiang
Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal decay rates on Jacobi expansion coefficients are derived, by applying van der Corput type le…
Levin methods for highly oscillatory integrals with singularities
Yinkun Wang, Shuhuang Xiang
In this paper, new Levin methods are presented for calculating oscillatory integrals with algebraic and/or logarithmic singularities. To avoid singularity, the technique of singula…
Sparse Solutions of a Class of Constrained Optimization Problems
Lei Yang, Xiaojun Chen, Shuhuang Xiang
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematical…
A Levin method for logarithmically singular oscillatory integrals
Yinkun Wang, Shuhuang Xiang
We propose a new stable Levin method to compute oscillatory integrals with logarithmic singularities and without stationary points. To avoid the singularity, we apply the technique…
Computation of highly oscillatory Bessel transforms with algebraic singularities
Zhenhua Xu, Shuhuang Xiang
In this paper, we consider the Clenshaw-Curtis-Filon method for the highly oscillatory Bessel transform , where is a smooth function on $[0, 1…
On Interpolation Approximation: Convergence rates for polynomial interpolation for functions of limited regularity
Shuhuang Xiang
The convergence rates on polynomial interpolation in most cases are estimated by Lebesgue constants. These estimates may be overestimated for some special points of sets for functi…
On Fast Implementation of Higher Order Hermite-Fejer Interpolation
Shuhuang Xiang, Guo He
The problem of barycentric Hermite interpolation is highly susceptible to overflows or underflows. In this paper, based on Sturm-Liouville equations for Jacobi orthogonal polynomia…
On the Optimal Rates of Convergence for Quadratures Derived from Chebyshev Points
Shuhuang Xiang
In this paper, we study the optimal general convergence rates for quadratures derived from Chebyshev points. By building on the aliasing errors on integration of Chebyshev polynomi…
On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity
Shuhuang Xiang, Folkmar Bornemann
We study the optimal general rate of convergence of the n-point quadrature rules of Gauss and Clenshaw-Curtis when applied to functions of limited regularity: if the Chebyshev coef…