Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

Handle URI:
http://hdl.handle.net/10754/626544
Title:
Smolyak's algorithm: A powerful black box for the acceleration of scientific computations
Authors:
Tempone, Raul ( 0000-0003-1967-4446 ) ; Wolfers, Soeren
Abstract:
We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak'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'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.
KAUST Department:
Applied Mathematics and Computational Science Program
Publisher:
arXiv
Issue Date:
26-Mar-2017
ARXIV:
arXiv:1703.08872
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1703.08872v2; http://arxiv.org/pdf/1703.08872v2
Appears in Collections:
Other/General Submission; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorTempone, Raulen
dc.contributor.authorWolfers, Soerenen
dc.date.accessioned2017-12-28T07:32:15Z-
dc.date.available2017-12-28T07:32:15Z-
dc.date.issued2017-03-26en
dc.identifier.urihttp://hdl.handle.net/10754/626544-
dc.description.abstractWe provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak'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'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.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1703.08872v2en
dc.relation.urlhttp://arxiv.org/pdf/1703.08872v2en
dc.rightsArchived with thanks to arXiven
dc.titleSmolyak's algorithm: A powerful black box for the acceleration of scientific computationsen
dc.typePreprinten
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.eprint.versionPre-printen
dc.identifier.arxividarXiv:1703.08872en
kaust.authorTempone, Raulen
kaust.authorWolfers, Soerenen
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