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

Raúl Tempone, Sören Wolfers*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

5 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computational Science and Engineering
PublisherSpringer Verlag
Pages201-228
Number of pages28
DOIs
StatePublished - 2018

Publication series

NameLecture Notes in Computational Science and Engineering
Volume123
ISSN (Print)1439-7358

ASJC Scopus subject areas

  • General Engineering
  • Computational Mathematics
  • Control and Optimization
  • Discrete Mathematics and Combinatorics
  • Modeling and Simulation

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