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- Daan Huybrechs, Stefan Vandewalle
- SIAM J. Numerical Analysis
- 2006

We consider the integration of one-dimensional highly oscillatory functions. Based on analytic continuation, rapidly converging quadrature rules are derived for a fairly general class of oscillatoryâ€¦ (More)

- Daan Huybrechs
- SIAM J. Numerical Analysis
- 2010

- Daan Huybrechs, Arno B. J. Kuijlaars, Nele Lejon
- Journal of Approximation Theory
- 2014

We study the limiting zero distribution of orthogonal polynomials with respect to some particular exponential weights eâˆ’nV (z) along contours in the complex plane. We are especially interested in theâ€¦ (More)

- Daan Huybrechs, Stefan Vandewalle
- SIAM J. Scientific Computing
- 2007

We consider two-dimensional scattering problems, formulated as an integral equation defined on the boundary of the scattering obstacle. The oscillatory nature of high-frequency scattering problemsâ€¦ (More)

- Alfredo DeaÃ±o, Daan Huybrechs, Arno B. J. Kuijlaars
- Journal of Approximation Theory
- 2010

In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of theseâ€¦ (More)

- Daan Huybrechs, Stefan Vandewalle
- Math. Comput.
- 2007

We present an efficient approach to evaluate multivariate highly oscillatory integrals on piecewise analytic integration domains. Cubature rules are developed that only require the evaluation of theâ€¦ (More)

- Daan Huybrechs, Sheehan Olver
- Foundations of Computational Mathematics
- 2012

Asymptotic expansions for oscillatory integrals typically depend on the values and derivatives of the integrand at a small number of critical points. We show that using values of the integrand atâ€¦ (More)

- Haiyong Wang, Daan Huybrechs, Stefan Vandewalle
- Math. Comput.
- 2014

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-called barycentricâ€¦ (More)

- Daan Huybrechs
- 2009

We obtain exponentially accurate Fourier series for non-periodic functions on the interval [âˆ’1, 1] by extending these functions to periodic functions on a larger domain. The series may be evaluated,â€¦ (More)

- Daan Huybrechs
- J. Computational Applied Mathematics
- 2009

Newton-Cotes quadrature rules are based on polynomial interpolation in a set of equidistant points. They are very useful in applications where sampled function values are only available on a regularâ€¦ (More)