Simple characterizations of exponential tractability for linear multivariate problems

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...

متن کامل

Tractability of multivariate analytic problems

In the theory of tractability of multivariate problems one usually studies problems with finite smoothness. Then we want to know which s-variate problems can be approximated to within ε by using, say, polynomially many in s and ε−1 function values or arbitrary linear functionals. There is a recent stream of work for multivariate analytic problems for which we want to answer the usual tractabili...

متن کامل

Generalized tractability for multivariate problems Part I: Linear tensor product problems and linear information

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...

متن کامل

Exponential convergence and tractability of multivariate integration for Korobov spaces

In this paper we study multivariate integration for a weighted Korobov space for which the Fourier coefficients of the functions decay exponentially fast. This implies that the functions of this space are infinitely times differentiable. Weights of the Korobov space monitor the influence of each variable and each group of variables. We show that there are numerical integration rules which achie...

متن کامل

Tractability of Approximating Multivariate Linear Functionals

We review selected tractability results for approximating linear tensor product functionals defined over reproducing kernel Hilbert spaces. This review is based on Volume II of our book [5] Tractability of Multivariate Problems. In particular, we show that all non-trivial linear tensor product functionals defined over a standard tensor product unweighted Sobolev space suffer the curse of dimens...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Complexity

سال: 2019

ISSN: 0885-064X

DOI: 10.1016/j.jco.2018.10.004