Generalized Tractability for Multivariate Problems Part II: Linear Tensor Product Problems, Linear Information, and Unrestricted Tractability
نویسندگان
چکیده
منابع مشابه
Generalized Tractability for Multivariate Problems Part II: Linear Tensor Product Problems, Linear Information, and Unrestricted Tractability
We continue the study of generalized tractability initiated in our previous paper “Generalized tractability for multivariate problems, Part I: Linear tensor product problems and linear information”, J. Complexity, 23, 262-295 (2007). We study linear tensor product problems for which we can compute linear information which is given by arbitrary continuous linear functionals. We want to approxima...
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Many papers study polynomial tractability for multivariate problems. Let n(ε, d) be the minimal number of information evaluations needed to reduce the initial error by a factor of ε for amultivariate problem defined on a space of d-variate functions. Here, the initial error is the minimal error that can be achieved without sampling the function. Polynomial tractability means that n(ε, d) is bou...
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It has been an open problem to derive a necessary and sufficient condition for a linear tensor product problem to be weakly tractable in the worst case. The complexity of linear tensor product problems in the worst case depends on the eigenvalues {λi}i∈N of a certain operator. It is known that if λ1 = 1 and λ2 ∈ (0, 1) then λn = o((lnn)−2), as n → ∞, is a necessary condition for a problem to be...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2009
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-009-9044-6