TY - CHAP
T1 - Smolyak’s Algorithm: A Powerful Black Box for the Acceleration of Scientific Computations
AU - Tempone, Raul
AU - Wolfers, Sören
N1 - KAUST Repository Item: Exported on 2020-04-23
PY - 2018/6/21
Y1 - 2018/6/21
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/630444
UR - https://link.springer.com/chapter/10.1007%2F978-3-319-75426-0_9
UR - http://www.scopus.com/inward/record.url?scp=85048947523&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-75426-0_9
DO - 10.1007/978-3-319-75426-0_9
M3 - Chapter
AN - SCOPUS:85048947523
SN - 9783319754253
SP - 201
EP - 228
BT - Lecture Notes in Computational Science and Engineering
PB - Springer Nature
ER -