The resolution of the Gibbs phenomenon for ``spliced'' functions in one and two dimensions (Q1368457)

Methods that eliminate the Gibbs phenomenon for analytic but non-periodic functions in one variable by employing the Gegenbauer polynomials [cf. \textit{D. Gottlieb, C.-W. Shu, A. Solomonoff} and \textit{H. Vandeven}, J. Comput. Appl. Math. 43, No. 1-2, 81-98 (1992; Zbl 0781.42022)] or the Bernoulli polynomials [cf. \textit{K. S. Eckhoff}, Math. Comput. 64, No. 210, 671-690 (1995; Zbl 0830.65144)] have been developed earlier. Extending these methods the authors provide here accurate reconstruction of ``spliced'' functions in full domain. For the bivariate case the authors prove exponential convergence of the Gegenbauer method.