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International Journal for Uncertainty Quantification

Publication de 6  numéros par an

ISSN Imprimer: 2152-5080

ISSN En ligne: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

Indexed in

A STOPPING CRITERION FOR ITERATIVE SOLUTION OF STOCHASTIC GALERKIN MATRIX EQUATIONS

Volume 6, Numéro 3, 2016, pp. 245-269
DOI: 10.1615/Int.J.UncertaintyQuantification.2016016463
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RÉSUMÉ

In this paper we consider generalized polynomial chaos (gPC) based stochastic Galerkin approximations of linear random algebraic equations where the coefficient matrix and the right-hand side are parametrized in terms of a finite number of i.i.d random variables. We show that the standard stopping criterion used in Krylov methods for solving the stochastic Galerkin matrix equations resulting from gPC projection schemes leads to a substantial number of unnecessary and computationally expensive iterations which do not improve the solution accuracy. This trend is demonstrated by means of detailed numerical studies on symmetric and nonsymmetric linear random algebraic equations. We present some theoretical analysis for the special case of linear random algebraic equations with a symmetric positive definite coefficient matrix to gain more detailed insight into this behavior. Finally, we propose a new stopping criterion for iterative Krylov solvers to avoid unnecessary iterations while solving stochastic Galerkin matrix equations. Our numerical studies suggest that the proposed stopping criterion can provide up to a threefold reduction in the computational cost.

CITÉ PAR
  1. Audouze Christophe, Nair Prasanth B., Sparse approximate solutions to stochastic Galerkin equations, Comptes Rendus Mathematique, 357, 6, 2019. Crossref

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