Asymptotic Behavior of the Eckhoff Approximation in Bivariate Case (Analysis in Theory and Applications, 2012)
The paper considers the Krylov-Lanczos and the Eckhoff approximations for recovering a bivariate function using limited number of its Fourier coefficients. These approximations are based on certain corrections associated with jumps in the partial derivatives of the approximated function. Approximation of the exact jumps is accomplished by solution of systems of linear equations along the idea of Eckhoff. Asymptotic behaviors of the approximate jumps and the Eckhoff approximation are studied. Exact constants of the asymptotic errors are computed. Numerical experiments validate theoretical investigations.
Keywords: Krylov-Lanczos approximation; Eckhoff approximation; Bernoulli polynomials; convergence acceleration.