Complexity of Local Solution of Multivariate Integral Equations
نویسنده
چکیده
In this paper the complexity of the local solution of Fredholm integral equations is studied. For certain Sobolev classes of multivariate periodic functions with dominating mixed derivative we prove matching lower and upper bounds. The lower bound is shown using relations to s-numbers. The upper bound is proved in a constructive way providing an implementable algorithm of optimal order based on Fourier coeecients and a hyperbolic cross approximation.
منابع مشابه
Complexity of Local Solution of Integral Equations
We study the complexity of local solution of Fredholm integral equations. This means that we want to compute not the full solution, but rather a functional (weighted mean, value in a point) of it. For certain Sobolev classes of multivariate periodic functions we prove matching upper and lower bounds and construct an algorithm of the optimal order, based on Fourier coeecients and a hyperbolic cr...
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ورودعنوان ژورنال:
- J. Complexity
دوره 11 شماره
صفحات -
تاریخ انتشار 1995