Blending Approximations with Sine Functions
Günter Baszeński, Franz-Jürgen Delvos, Sebastian Jester · Birkhäuser Basel eBooks · 1992
We consider sine double series expansions of functions defined on the unit square. We derive error estimates for partial sums and for interpolating sine polynomials assuming that the asymptotic growth of the series coefficients is known. The constants in the error estimates are explicitly computed. We show that Boolean sums yield almost the same asymptotic error estimates as the conventional tensor product approach but with a reduced number of terms. An example is given which shows that the asymptotic error (when the number of points increases) is exactly of the stated order. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.