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Accuracy of Numerical Solution to Dynamic Programming Models

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  • King, Robert P.
  • Lohano, Heman D.

Abstract

Dynamic programming models with continuous state and control variables are solved approximately using numerical methods in most applications. We develop a method for measuring the accuracy of numerical solution of stochastic dynamic programming models. Using this method, we compare the accuracy of various interpolation schemes. As expected, the results show that the accuracy improves as number of nodes is increased. Comparison of Chebyshev and linear spline indicates that the linear spline may give higher maximum absolute error than Chebyshev, however, the overall performance of spline interpolation is better than Chebyshev interpolation for non-smooth functions. Two-stage grid search method of optimization is developed and examined with accuracy analysis. The results show that this method is more efficient and accurate. Accuracy is also examined by allocating a different number of nodes for each dimension. The results show that a change in node configuration may yield a more efficient and accurate solution.

Suggested Citation

  • King, Robert P. & Lohano, Heman D., 2006. "Accuracy of Numerical Solution to Dynamic Programming Models," Staff Papers 14230, University of Minnesota, Department of Applied Economics.
    • Handle: RePEc:ags:umaesp:14230
    DOI: 10.22004/ag.econ.14230
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    Cited by:

    1. Heman D. Lohano & Robert P. King, 2009. "A Stochastic Dynamic Programming Analysis of Farmland Investment and Financial Management," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 57(4), pages 575-600, December.

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