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

Kenneth Judd, Lilia Maliar, Serguei Maliar and Rafael Valero ()

No 19326, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: 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.

JEL-codes: C63 C68 (search for similar items in EconPapers)
Date: 2013-08
Note: TWP
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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.

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Related works:
Journal Article: Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain (2014)
Working Paper: Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain (2013)
Working Paper: Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain (2013)
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