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Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain

  • Kenneth L. Judd
  • Lilia Maliar
  • Serguei Maliar
  • Rafael Valero

First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given economic model. Finally, we advocate the use of low-cost fixed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth models, we find that the proposed techniques lead to substantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic economic models.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 19326.

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Date of creation: Aug 2013
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Publication status: published as Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
Handle: RePEc:nbr:nberwo:19326
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