Computable Error Bounds for the Nystroem Method.

摘要

The classical Nystroem method for the numerical solution of Fredholm integral equations of second kind consists of numerical integration, collocation, and interpolation. The approximate solution obtained by this procedure is shown to be identical to the solution of certain finite-rank integral equations with kernels belonging to a specified class (K sub n), and thus has minimal error with respect to approximation of the original equation over this class. A computable (but in general nonoptimal) error bound for the Nystroem approximate solution can be obtained on the basis of how well a specific finite-rank integral operator with kernel in (K sub n) approximates the integral operator in the Fredholm equation being solved numerically. (Author)