5 citations · 32 across the 21 of their papers we have counts for
21 papers
Hermite spectral approximation for functions with endpoint singularities using exponential transforms
Haiyong Wang
In this paper we introduce Hermite spectral approximation for functions with endpoint singularities using exponential transforms, including single exponential (SE), double exponent…
Superconvergence points of Hermite spectral interpolation
Haiyong Wang, Zhimin Zhang
Hermite spectral method plays an important role in the numerical simulation of various partial differential equations (PDEs) on unbounded domains. In this work, we study the superc…
On the deterioration of convergence rate of spectral differentiations for functions with singularities
Haiyong Wang
Spectral differentiations are basic ingredients of spectral methods. In this work, we analyze the pointwise rate of convergence of spectral differentiations for functions containin…
Convergence analysis of Hermite approximations for analytic functions
Haiyong Wang, Lun Zhang
In this paper, we present a rigorous analysis of root-exponential convergence of Hermite approximations, including projection and interpolation methods, for functions that are anal…
Convergence analysis of Laguerre approximations for analytic functions
Haiyong Wang
Laguerre spectral approximations play an important role in the development of efficient algorithms for problems in unbounded domains. In this paper, we present a comprehensive conv…
An efficient spectral method for the fractional Schrödinger equation on the real line
Mengxia Shen, Haiyong Wang
The fractional Schrödinger equation (FSE) on the real line arises in a broad range of physical settings and their numerical simulation is challenging due to the nonlocal nature and…
New error bounds for Legendre approximations of differentiable functions
Haiyong Wang
In this paper we present a new perspective on error analysis of Legendre approximations for differentiable functions. We start by introducing a sequence of Legendre-Gauss-Lobatto p…
Analysis of error localization of Chebyshev spectral approximations
Haiyong Wang
Chebyshev spectral methods are widely used in numerical computations. When the underlying function has a singularity, it has been observed by L. N. Trefethen in 2011 that its Cheby…
Optimal rates of convergence and error localization of Gegenbauer projections
Haiyong Wang
Motivated by comparing the convergence behavior of Gegenbauer projections and best approximations, we study the optimal rate of convergence for Gegenbauer projections in the maximu…
How much faster does the best polynomial approximation converge than Legendre projection?
Haiyong Wang
We compare the convergence behavior of best polynomial approximations and Legendre and Chebyshev projections and derive optimal rates of convergence of Legendre projections for ana…
Analysis of multivariate Gegenbauer approximation in the hypercube
Haiyong Wang, Lun Zhang
In this paper, we are concerned with multivariate Gegenbauer approximation of functions defined in the -dimensional hypercube. Two new and sharper bounds for the coefficients of…
A new and sharper bound for Legendre expansion of differentiable functions
Haiyong Wang
In this paper, we provide a new and sharper bound for the Legendre coefficients of differentiable functions and then derive a new error bound of the truncated Legendre series in th…
A unified framework for asymptotic analysis and computation of finite Hankel transform
Haiyong Wang
In this paper we present a unified framework for asymptotic analysis and computation of the finite Hankel transform. This framework enables us to derive asymptotic expansions of th…
Jacobi polynomials on the Bernstein ellipse
Haiyong Wang, Lun Zhang
In this paper, we are concerned with Jacobi polynomials on the Bernstein ellipse with motivation mainly coming from recent studies of convergence rate of spectral…
On the optimal estimates and comparison of Gegenbauer expansion coefficients
Haiyong Wang
In this paper, we study optimal estimates and comparison of the coefficients in the Gegenbauer series expansion. We propose an alternative derivation of the contour integral repres…
Fast and highly accurate computation of Chebyshev expansion coefficients of analytic functions
Haiyong Wang, Daan Huybrechs
Chebyshev expansion coefficients can be computed efficiently by using the FFT, and for smooth functions the resulting approximation is close to optimal, with computations that are…
Convergence rate and acceleration of Clenshaw-Curtis quadrature for functions with endpoint singularities
Haiyong Wang
In this paper, we investigate the rate of convergence of Clenshaw-Curtis quadrature and its acceleration for functions with endpoint singularities in X^s, where X^s denotes the spa…
On Fast Implementation of Clenshaw-Curtis and Fejér-type Quadrature Rules
Shuhaung Xiang, Guo He, Haiyong Wang
Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, DCT and IDST, respectively, together with the efficient evalua…
A Gaussian quadrature rule for oscillatory integrals on a bounded interval
Andreas Asheim, Alfredo Deaño, Daan Huybrechs +1
We investigate a Gaussian quadrature rule and the corresponding orthogonal polynomials for the oscillatory weight function on the interval . We show that such a r…
Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials
Haiyong Wang, Daan Huybrechs, Stefan Vandewalle
Barycentric interpolation is arguably the method of choice for numerical polynomial interpolation. The polynomial interpolant is expressed in terms of function values using the so-…
Asymptotic expansions and fast computation of oscillatory Hilbert transforms
Haiyong Wang, Lun Zhang, Daan Huybrechs
In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form $$H^{+}(f(t)e^{iωt})(x)=-int_{0}^{\infty}e^{iωt}\frac{f(t)}…