Journal article
Mathematical Properties of Polynomial Dimensional Decomposition
SIAM/ASA journal on uncertainty quantification, Vol.6(2), pp.816-844
01/2018
DOI: 10.1137/16M1109382
Abstract
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This study constructs dimensionwise and orthogonal splitting of polynomial spaces, proves completeness of polynomial orthogonal basis for prescribed assumptions, and demonstrates mean-square convergence to the correct limit—all associated with PDD. A second-moment error analysis reveals that PDD cannot commit larger error than polynomial chaos expansion (PCE) for the appropriately chosen truncation parameters. From the comparison of computational efforts, required to estimate with the same precision the variance of an output function involving exponentially attenuating expansion coefficients, the PDD approximation can be markedly more efficient than the PCE approximation.
Details
- Title: Subtitle
- Mathematical Properties of Polynomial Dimensional Decomposition
- Creators
- Sharif Rahman
- Resource Type
- Journal article
- Publication Details
- SIAM/ASA journal on uncertainty quantification, Vol.6(2), pp.816-844
- DOI
- 10.1137/16M1109382
- ISSN
- 2166-2525
- eISSN
- 2166-2525
- Grant note
- DOI: 10.13039/100000147, name: Division of Civil, Mechanical and Manufacturing Innovation, award: CMMI-1462385
- Language
- English
- Date published
- 01/2018
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984196637502771
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