A new fluctuation expansion based method for the univariate numerical integration under Gaussian weights

Authors:
Metin Demiralp
Affiliations:
Informatics Institute, Istanbul Technical University, Maslak, Turkey
Venue:
MATH'05 Proceedings of the 8th WSEAS International Conference on Applied Mathematics
Year:
2005

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Abstract

This paper presents a new method based on quite recently proposed fluctuation expansion for the evaluation of certain operators' expectation values over Hilbert spaces. The fluctuation expansion has been constructed with the aid of a projection operator which projects to a one dimensional subspace of the Hilbert space under consideration. We, now, extend this idea to the utilization of projections to multidimensional subspace of the same Hilbert space. We take a univariate integral under a Gaussian weight (that is, bell like shaped function) and keep only zeroth order terms which contain no fluctuation functions. After some matrix algebraic manipulations we obtain an interpolation formula as a linear combination of the integral's kernel function's values at the eigenvalues of the matrix which is a upperleftmost truncation from the matrix representation of the independent variable.