On the accuracy of the polynomial chaos approximation for random variables and stationary stochastic processes.

By R. Field, Mircea Dan Grigoriu. 2003

153 citations recorded by the source corpus.

Subfields: Environmental Engineering, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6e55c6898d43db7bd7a947480905f52bfc70d140

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In Environmental Engineering

In Global and Planetary Change

In Statistics and Probability

Citations in the corpus

Simulation of simply cross correlated random fields by series expansion methods (2008, background): “Grigoriu [3] criticize the algorithm for its computational intensity and questionable accuracy.”
Uncertainty analysis of complex structural systems (2009, background): “Since in practical application the number P is necessarily finite, and also sufficiently small to be competitive with simple ‘direct’ MCS, the rate of convergence plays an important role [14].”
A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes (2007, background): “It was shown in [ 15 ] and [16] that for functions involving high nonlinearities and critical points the GPCE fails to perform satisfactorily.”
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2010, background): “in [30] for evaluating a posteriori the accuracy of truncated PC expansions.”
Geotechnical probabilistic analysis by collocation-based stochastic response surface method: An Excel add-in implementation (2009, background): “The accuracy of these truncated low-order expansions are discussed elsewhere (Field and Grigoriu 2004, Debusschere et al. 2004).”
Evaluating the response statistics of an uncertain bridge–vehicle system (2012, background): “An increase in the order of PCE cannot improve the accuracy, which may be due to the limitation of the PC approximations [37].”
A stochastic finite element procedure for moment and reliability analysis (2006, methodology): “Projection method This method was used by (Puiget al., 2002, Xiu and Karniadakis, 2002, Field and Grigoriu, 2004).”