On the fast and fully discretized solution of integral and pseudo-differential equations on smooth curves
The paper is devoted to the numerical solution of pseudo-differential equations on smooth closed curves by a fully discrete version of the trigonometric Galerkin method. For the discrete Galerkin equations, approximate solutions with small residuals are considered, and optimal error estimates in periodic Sobolev norms are obtained. Using the conjugate gradient method of Hestenes and Stiefel applied to the normal equations, the authors provide an iteration scheme where the approximations can be obtained by a total number of \(O(N\log N)\) arithmetical operations. The influence of noise in the model of the problem as well as in the right-hand side is examined, and some numerical examples are presented.
scientific article; zbMATH DE number 1846808