Abstract:
This paper is devoted to the solution of linear Fredholm equations in the unit $s$-dimensional cube for classes of functions with a dominant mixed derivative of order $r$ in each variable. We present an algorithm for obtaining the solution over the whole domain with an error $O(N^{-r}\ln^{2s-1}N)$ in the uniform metric using the values of the given functions at $O(N\ln^{2s-1}N)$ points and consisting of $O(N\ln^{2s-1}N)$ elementary operations. We show that these estimates can only be improved at the expense of the exponent of $\ln N$.
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