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Approximation complexity of additive random fields. / Lifshits, M. A.; Zani, M.

In: Journal of Complexity, Vol. 24, No. 3, 01.01.2008, p. 362-379.

Research output: Contribution to journal › Article › peer-review

Harvard

Lifshits, MA & Zani, M 2008, 'Approximation complexity of additive random fields', Journal of Complexity, vol. 24, no. 3, pp. 362-379. https://doi.org/10.1016/j.jco.2007.11.002

APA

Lifshits, M. A., & Zani, M. (2008). Approximation complexity of additive random fields. Journal of Complexity, 24(3), 362-379. https://doi.org/10.1016/j.jco.2007.11.002

Vancouver

Lifshits MA, Zani M. Approximation complexity of additive random fields. Journal of Complexity. 2008 Jan 1;24(3):362-379. https://doi.org/10.1016/j.jco.2007.11.002

Author

Lifshits, M. A. ; Zani, M. / Approximation complexity of additive random fields. In: Journal of Complexity. 2008 ; Vol. 24, No. 3. pp. 362-379.

BibTeX

@article{ba6bdab00fa644ddb7a8b17670a24646,
title = "Approximation complexity of additive random fields",
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) ξk (ω) φ{symbol}k (t) .The results are obtained in the asymptotic setting d → ∞ as suggested by Wo{\'z}niakowski [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 Vd, and we find the explosion coefficient V.",
keywords = "Approximation complexity, Curse of dimensionality, Gaussian processes, Linear approximation error, Random fields, Tractability",
author = "Lifshits, {M. A.} and M. Zani",
year = "2008",
month = jan,
day = "1",
doi = "10.1016/j.jco.2007.11.002",
language = "English",
volume = "24",
pages = "362--379",
journal = "Journal of Complexity",
issn = "0885-064X",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - Approximation complexity of additive random fields

AU - Lifshits, M. A.

AU - Zani, M.

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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) ξk (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 Vd, and we find the explosion coefficient V.

AB - 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) ξk (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 Vd, and we find the explosion coefficient V.

KW - Approximation complexity

KW - Curse of dimensionality

KW - Gaussian processes

KW - Linear approximation error

KW - Random fields

KW - Tractability

UR - http://www.scopus.com/inward/record.url?scp=44649166470&partnerID=8YFLogxK

U2 - 10.1016/j.jco.2007.11.002

DO - 10.1016/j.jco.2007.11.002

M3 - Article

AN - SCOPUS:44649166470

VL - 24

SP - 362

EP - 379

JO - Journal of Complexity

JF - Journal of Complexity

SN - 0885-064X

IS - 3

ER -

ID: 37009940