Analysis of series with stochastic coefficients

R. Dekeyser, F. Iglói, F. Mallezie, F. Seno

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

For functions with power-law singularities we consider series expansions whose coefficients have been determined by Monte Carlo simulation. In many practical problems the relative noise of the coefficients is constant or slowly increasing with the order. We modeled real Monte Carlo expansions by test series with known singularity structure where noise with different strength and form is imposed on the coefficients. The efficiency of different standard methods of series analysis (ratio method, Padé approximants, differential approximants) has been tested together with smoothing methods based on repeated partial summation of the series. We found the Padé method to give reasonable estimates and its accuracy is independent of the smoothing, while the estimates of the ratio and the differential approximant methods are greatly improved when smoothing is applied. Indeed, we found the ratio method with optimally selected smoothing to give the most reliable results.

Original languageEnglish
Pages (from-to)1923-1930
Number of pages8
JournalPhysical Review A
Volume42
Issue number4
DOIs
Publication statusPublished - 1990

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smoothing
coefficients
estimates
series expansion
expansion
simulation

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Analysis of series with stochastic coefficients. / Dekeyser, R.; Iglói, F.; Mallezie, F.; Seno, F.

In: Physical Review A, Vol. 42, No. 4, 1990, p. 1923-1930.

Research output: Contribution to journalArticle

Dekeyser, R, Iglói, F, Mallezie, F & Seno, F 1990, 'Analysis of series with stochastic coefficients', Physical Review A, vol. 42, no. 4, pp. 1923-1930. https://doi.org/10.1103/PhysRevA.42.1923
Dekeyser, R. ; Iglói, F. ; Mallezie, F. ; Seno, F. / Analysis of series with stochastic coefficients. In: Physical Review A. 1990 ; Vol. 42, No. 4. pp. 1923-1930.
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