Computational complexity of the integration problem for anisotropic classes
There is an increasing interest in studying the computational complexity of high-dimensional integration due to its applications in computational mathematics, finance, physics, engineering and in statistics. The author studies this problem in a considerable generality. More precisely, by developing a decomposition technique of Borel measure on the unit cube of a \(d\)-dimensional Euclidean space, he determines the exact order of \(\epsilon\)--complexity of the numerical integration problem for the anisotropic class \(W_\infty^r(I^d)\) and \(H_\infty^r(I^d)\). In addition, by the imbedding relationship between function classes, he extends the results to the classes of functions \(W_p^{\wedge}(I^d)\) and \(H_p^{\wedge}(I^d)\).
scientific article; zbMATH DE number 2170081
scientific article