## Abstract

Let X (t, ω) be an additive random field for (t, ω) ∈ [0, 1]^{d} × Ω. We investigate the complexity of finite rank approximationX (t, ω) ≈ underover(∑, k = 1, n) ξ_{k} (ω) φ{symbol}_{k} (t) .The results are obtained in the asymptotic setting d → ∞ as suggested by Woźniakowski [Tractability and strong tractability of linear multivariate problems, J. Complexity 10 (1994) 96-128.]; [Tractability for multivariate problems for weighted spaces of functions, in: Approximation and Probability. Banach Center Publications, vol. 72, Warsaw, 2006, pp. 407-427.]. They provide quantitative version of the curse of dimensionality: we show that the number of terms in the series needed to obtain a given relative approximation error depends exponentially on d. More precisely, this dependence is of the form V^{d}, and we find the explosion coefficient V.

Original language | English |
---|---|

Pages (from-to) | 362-379 |

Number of pages | 18 |

Journal | Journal of Complexity |

Volume | 24 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2008 |

## Scopus subject areas

- Algebra and Number Theory
- Statistics and Probability
- Numerical Analysis
- Control and Optimization
- Applied Mathematics