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

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

Working Papers. Serie AD from Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie)

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.

Keywords: Smolyak method; sparse grid; adaptive domain; projection; anisotropic grid; collocation; high-dimensional problem (search for similar items in EconPapers)
JEL-codes: C63 C68 (search for similar items in EconPapers)
Pages: 50 pages
Date: 2013-09
New Economics Papers: this item is included in nep-cmp and nep-dge
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Published by Ivie

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http://www.ivie.es/downloads/docs/wpasad/wpasad-2013-06.pdf Fisrt version / Primera version, 2013 (application/pdf)

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