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Smolyak’s Algorithm: A Powerful Black Box for the Acceleration of Scientific Computations

  • Raúl Tempone
  • Sören WolfersEmail author
Conference paper
  • 373 Downloads
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 123)

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.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.King Abdullah University of Science and Technology (KAUST)ThuwalKingdom of Saudi Arabia

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