Tractability of Tensor Product Linear Operators
نویسندگان
چکیده
منابع مشابه
Tractability of Tensor Product Linear Operators
This paper deals with the worst case setting for approximating multivariate tensor product linear operators defined over Hilbert spaces. Approximations are obtained by using a number of linear functionals from a given class of information. We consider the three classes of information: the class of all linear functionals, the Fourier class of inner products with respect to given orthonormal elem...
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We study tractability in the worst case setting of tensor product linear operators defined over weighted tensor product Hilbert spaces. Tractability means that the minimal number of evaluations needed to reduce the initial error by a factor of ε in the d-dimensional case has a polynomial bound in both ε−1 and d. By one evaluation we mean the computation of an arbitrary continuous linear functio...
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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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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: Journal of Complexity
سال: 1997
ISSN: 0885-064X
DOI: 10.1006/jcom.1997.0454