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

  • Kenneth L. Judd

    (Hoover Institution, Stanford University)

  • Lilia Maliar

    (Department of Economics, Stanford University)

  • Serguei Maliar

    (Department of Economics, Stanford University)

  • Rafael Valero

    (University of Alicante)

First, we propose a more e¢ cient implementation of the Smolyak method for inter- polation, 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 e¤ectively adapt the Smolyak hyper- cube to a solution domain of a given economic model. Finally, we advocate the use of low-cost .xed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth models, we .nd that the proposed techniques lead to sub- stantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic economic models.

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Paper provided by Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory in its series BYU Macroeconomics and Computational Laboratory Working Paper Series with number 2013-02.

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Length: 47 pages
Date of creation: Aug 2013
Date of revision:
Publication status: Published as "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," in Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
Handle: RePEc:byu:byumcl:201302
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