Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain

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

Journal of Economic Dynamics and Control, 2014, vol. 44, issue C, 92-123

Abstract: We show how to enhance the performance of a Smolyak method for solving dynamic economic models. 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 that allow 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 argue that in large-scale economic applications, a solution algorithm based on Smolyak interpolation has substantially lower expense when it uses derivative-free fixed-point iteration instead of standard time iteration. In the context of one- and multi-agent optimal growth models, we find that the proposed modifications to the conventional Smolyak method lead to substantial increases in accuracy and speed.

Keywords: Smolyak method; Sparse grid; Adaptive domain; Projection; Anisotropic grid; High-dimensional problem (search for similar items in EconPapers)
JEL-codes: C63 C68 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (71)

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Related works:
Software Item: Smolyak code for "Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain" (2015)
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)
Working Paper: Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:44:y:2014:i:c:p:92-123

DOI: 10.1016/j.jedc.2014.03.003

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