Smolyak’s Algorithm: A Powerful Black Box for the Acceleration of Scientific Computations
Type
Book ChapterAuthors
Tempone, Raul
Wolfers, Sören
KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
Date
2018-06-20Online Publication Date
2018-06-21Print Publication Date
2018Embargo End Date
2019-06-21Permanent link to this record
http://hdl.handle.net/10754/630444
Metadata
Show full item recordAbstract
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.Citation
Tempone R, Wolfers S (2018) Smolyak’s Algorithm: A Powerful Black Box for the Acceleration of Scientific Computations. Sparse Grids and Applications - Miami 2016: 201–228. Available: http://dx.doi.org/10.1007/978-3-319-75426-0_9.Publisher
Springer NaturearXiv
1703.08872Additional Links
https://link.springer.com/chapter/10.1007%2F978-3-319-75426-0_9http://arxiv.org/pdf/1703.08872
ae974a485f413a2113503eed53cd6c53
10.1007/978-3-319-75426-0_9