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Projection Methods and the Curse of Dimensionality
University of Augsburg and CESIfo, Augsburg, Germany
University of Augsburg, Augsburg, Germany
- 1 University of Augsburg and CESIfo, Augsburg, Germany
- 2 University of Augsburg, Augsburg, Germany
Journal of Mathematical Finance·Volume 08 (2018)·Pages 317–334·Published 29 March 2018·DOI10.4236/jmf.2018.82021
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Abstract
We study the ability of three different projection methods to solve high-dimensional state space problems: Galerkin, collocation, and least squares projection. The curse of dimensionality can be reduced substantially for both Least Squares and Galerkin projection methods through the use of monomial formulas. Least Squares are shown to require a good initial value in order to give an accurate solution. Alternatively, we suggest a new ad hoc collocation method for complete polynomials that is fast and easy to implement.
KeywordsProjection MethodsGalerkinCollocationLeast SquaresHeterogeneous AgentsStochastic Dynamic General Equilibrium
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