Solving SDGE Models: A New Algorithm for the Sylvester Equation

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.

[1]  Stepan Jurajda,et al.  Anatomy of the Czech Labour Market:From Over-Employment to Under-Employment in Ten Years? , 2004 .

[2]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[3]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[4]  G. Stewart,et al.  An Algorithm for Computing Reducing Subspaces by Block Diagonalization. , 1979 .

[5]  He-hui Jin,et al.  Perturbation methods for general dynamic stochastic models , 2002 .

[6]  Jack J. Dongarra,et al.  Numerical Considerations in Computing Invariant Subspaces , 1992, SIAM J. Matrix Anal. Appl..

[7]  Richard H. Bartels,et al.  Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4] , 1972, Commun. ACM.

[8]  T. Holub,et al.  Foreign Exchange Interventions Under Inflation Targeting: The Czech Experience , 2006 .

[9]  Roman Horvath,et al.  Exchange Rate Variability, Pressures and Optimum Currency Area Criteria: Implications for the Central and Eastern European Countries , 2005 .

[10]  Antony Jameson,et al.  Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix , 1968 .

[11]  Ian Babetskii.  EU Enlargement and Endogeneity of some OCA Criteria: Evidence from the CEECs , 2004 .

[12]  Ellen R. McGrattan,et al.  Mechanics of forming and estimating dynamic linear economies , 1994 .

[13]  Monetary Policy and the Term Spread in a Macro Model of a Small Open Economy , 2002 .

[14]  Gene H. Golub,et al.  Matrix computations , 1983 .