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

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Author Info

  • Kenneth Judd

    ()
    (Hoover Institution)

  • Lilia Maliar

    ()
    (Universidad de Alicante)

  • Rafael Valero

    ()
    (Dpto. Fundamentos del Análisis Económico)

  • Serguei Maliar

    (Universidad de Alicante)

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.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2013-06.pdf
File Function: Fisrt version / Primera version, 2013
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2013-06.

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Length: 50 pages
Date of creation: Sep 2013
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2013-06

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Keywords: Smolyak method; sparse grid; adaptive domain; projection; anisotropic grid; collocation; high-dimensional problem;

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