Interpolation and cubature approximations and analysis for a class of wideband integrals on the sphere (Q380978)

The article is devoted to the area of computer mathematics. A method of evaluation of generalized Fourier integrals on the sphere is presented. Denote the wavenumber of the generalized Fourier integral by \(k\). Let on the sphere be \(2N^2\) cubature points. The authors prove that the error of the presented method is \(O(k^{-\ell}N^{-r})\). Where \(\ell= 0,1,2\), and \(r_\ell> 0\), \(r_\ell\) depends on the smoothness of the integrands. Consequently, the quality of the presented method for a computation of highly-oscillatory integrals is improved, when the wavenumber is increasing. There are some numerical results.