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Stochastic Collocation Methods: A Survey

In: Handbook of Uncertainty Quantification

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  • Dongbin Xiu

    (University of Utah, Department of Mathematics and Scientific Computing and Imaging Institute)

Abstract

Stochastic collocation (SC) has become one of the major computational tools for uncertainty quantification. Its primary advantage lies in its ease of implementation. To carry out SC, one needs only a reliable deterministic simulation code that can be run repetitively at different parameter values. And yet, the modern-day SC methods can retain the high-order accuracy properties enjoyed by most of other methods. This is accomplished by utilizing the large amount of literature in the classical approximation theory. Here we survey the major approaches in SC. In particular, we focus on a few well-established approaches: interpolation, regression, and pseudo projection. We present the basic formulations of these approaches and some of their major variations. Representative examples are also provided to illustrate their major properties.

Suggested Citation

  • Dongbin Xiu, 2017. "Stochastic Collocation Methods: A Survey," Springer Books, in: Roger Ghanem & David Higdon & Houman Owhadi (ed.), Handbook of Uncertainty Quantification, chapter 20, pages 699-716, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12385-1_26
    DOI: 10.1007/978-3-319-12385-1_26
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