Smolyak method for solving dynamic economic modelsLagrange interpolation, anisotropic grid and adaptive domain

  1. Kenneth L. Judd 1
  2. Lilia Maliar 1
  3. Serguei Maliar 1
  4. Rafael Valero 2
  1. 1 Stanford University
    info

    Stanford University

    Stanford, Estados Unidos

    ROR https://ror.org/00f54p054

  2. 2 Universitat d'Alacant
    info

    Universitat d'Alacant

    Alicante, España

    ROR https://ror.org/05t8bcz72

Revue:
Working papers = Documentos de trabajo: Serie AD

Année de publication: 2013

Número: 6

Pages: 1-49

Type: Working Paper

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Résumé

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.

La source de données: Dialnet