Computational Economics

, Volume 25, Issue 1–2, pp 167–187 | Cite as

Solving SDGE Models: A New Algorithm for the Sylvester Equation

  • OndŘej KamenÍk


This paper presents a new numerical algorithm for solving the Sylvester equation involved in higher-order perturbation methods developed for solving stochastic dynamic general equilibrium models. The new algorithm surpasses other methods used so far (including the very popular doubling algorithm) in terms of computational time, memory consumption, and numerical stability.


stochastic dynamic general equilibrium models high-order permutations computational algorithms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, E.W., et al. (1996). Mechanics of forming and estimating dynamic linear economies. In Handbook of Computational Economics, Vol. 1. Elsevier, Amsterdam.Google Scholar
  2. Bartels, R.H. and Stewart, G.W. (1972). Solution of the equation ax + xb = c. Communications of ACM, 15, 820–826.CrossRefGoogle Scholar
  3. Bavely, C.A. and Stewart, G.W. (1979). An algorithm for computing reducing subspaces by block diagonalization. SIAM Journal on Numerical Analysis, 16(2), 359–367.CrossRefGoogle Scholar
  4. Dongarra, J.J., Hammarling, S. and Wilkinson, J.H. (1992). Numerical considerations in computing invariant subspaces. SIAM Journal on Matrix Analysis and Applications, 13(1), 145–161.Google Scholar
  5. Golub, G.H. and Loan, C.F.V. (1996). Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, Maryland.Google Scholar
  6. Higham, N.J. (2002). Accuracy and Stability of Numerical Algorithms. SIAM, second edition.Google Scholar
  7. Jin, H.-H. and Judd, K. (2002). Perturbation methods for general dynamic stochastic models. Unpublished manuscript.Google Scholar
  8. Juillard, M. (2003). Solving stochastic dynamic equilibrium models: A $k$-order perturbation approach.
  9. Laxton, D. and Pesenti, P. (2003). Monetary rules for small, open, emerging economies. NBER Working Paper 9568.

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Monetary and Statistics DepartmentThe Czech National BankPrague 1Czech Republic

Personalised recommendations