@inbook{b992cf47d0a54655a66568ce068b8ca6,
title = "Smolyak{\textquoteright}s algorithm: A powerful black box for the acceleration of scientific computations",
abstract = "We provide a general discussion of Smolyak{\textquoteright}s algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak{\textquoteright}s work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak{\textquoteright}s algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner.",
author = "Ra{\'u}l Tempone and S{\"o}ren Wolfers",
note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.",
year = "2018",
doi = "10.1007/978-3-319-75426-0_9",
language = "English (US)",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer Verlag",
pages = "201--228",
booktitle = "Lecture Notes in Computational Science and Engineering",
address = "Germany",
}