Average Case Complexity Of Linear Multivariate Problems Part I: Theory (1991)
| Venue: | APPLICATIONS; J. COMPLEXITY |
| Citations: | 13 - 4 self |
BibTeX
@ARTICLE{Wozniakowski91averagecase,
author = {H. Wozniakowski},
title = {Average Case Complexity Of Linear Multivariate Problems Part I: Theory},
journal = {APPLICATIONS; J. COMPLEXITY},
year = {1991},
volume = {8},
pages = {373--392}
}
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Abstract
We study the average case complexity of linear multivariate problems, that is, the approximation of continuous linear operators on functions of d variables. The function spaces are equipped with Gaussian measures. We consider two classes of information. The first class std consists of function values, and the second class all consists of all continuous linear functionals. Tractability of a linear multivariate problem means that the average case complexity of computing an "-approximation is O ((1=") p ) with p independent of d. The smallest such p is called the exponent of the problem. Under mild assumptions, we prove that tractability in all is equivalent to tractability in std , and that the difference of the exponents is at most 2. The proof of this result is not constructive. We provide a simple condition to check tractability in all . We also address the issue how to construct optimal (or nearly optimal) sample points for linear multivariate problems. We use rela...
