Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
Accurate reconstructions of functions of finite regularity from truncated Fourier series expansions
Mathematics of Computation
On the Gibbs Phenomenon and Its Resolution
SIAM Review
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
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We present a spline approximation method for a piece of a surface where jump discontinuities occur along curves. The data for the surface is assumed to be Fourier coefficients which are limited in order and possibly contaminated with noise. The support of the approximation is bounded by three sides of a rectangle with a fourth boundary possibly curved. Discontinuities of the surface may occur across the curved side and linear sides adjacent to it. The approximation uses a small number of lines through the support and parallel to the straight boundary lines that are adjacent to the curve. Along each line a one-dimensional spline approximation is done for a section of the surface over the line. This approximation uses two-dimensional Fourier coefficient data, localizing spline functions, and a technique which we developed earlier for one-dimensional analogues of the problem. We use a spline quasi-interpolation scheme to create a surface approximation from the section approximations. The result is accurate even when the surface is discontinuous across the curved boundary and adjacent side boundaries.