In this paper we investigate whether the dynamic properties of the U.S. business cycle have changed in the last fifty years. For this purpose we develop a flexible business cycle indicator that is constructed from a moderate set of macroeconomic time series. The coincident economic indicator is...

The Helmholtz equation is considered. The matrices decomposition algorithms for Legendre spectral collocation approximation, which nearly reduce a half of scale for original discrete system, are achieved by the centrosymmetry and positivity. Also, the di erence and finite element preconditioning...