Information complexity of multivariate Fredholm integral equations in Sobolev classes
Information-based complexity theory studies the difficulty of the approximate solution of numerical problems for which the information is partial, contaminated, and priced. Determining the information complexity of the basic problems of mathematical physics is a principal goal of information-based complexity theory. One of these basic problems is the solution of Fredholm integral equations of the second kind. The authors determine the exact order information complexity for Fredholm equations with kernels from Sobolev classes using a Gelfand number technique. An algorithm of optimal order, based on Fourier coefficients and a hyperbolic cross approximation of the kernel function is derived. Numerical examples are given.
Fredholm integral equations of the second kind
scientific article; zbMATH DE number 884755