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 -