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Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/ analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional… (More)

The Schatten p-norm condition of the discrete-time Lyapunov operator L A defined on matrices P 2 R nn by L A P P ? APA T is studied for stable matrices A 2 R nn. Bounds are obtained for the norm of L A and its inverse that depend on the spectrum, singular values and radius of stability of A. Since the solution P of the the discrete-time algebraic Lyapunov… (More)

New upper bounds for the solution of the discrete algebraic Lyapunov equation (DALE) P = APA T + Q are presented. The only restriction on their applicability is that A be stable; there are no restrictions on the singular values of A nor on the diagonalizability of A. The new bounds relate the size of P to the radius of stability of A. The upper bounds are… (More)

A family of sharp, arbitrarily tight, upper and lower matrix bounds for solutions of the discrete algebraic Lyapunov are presented. The lower bounds are tighter than previously known ones. Unlike the majority of previously known upper bounds, those derived here have no restrictions on their applicability. Upper and lower bounds for individual eigenvalues… (More)

This paper analyzes traveling wave profiles possessing an internal resonance point for a class of systems of partial differential equations describing oxidation and vaporization of liquid fuel in a porous medium when an oxidizer (air) is injected. It is shown that the resonance is characterized by a saddle point of an associated vector field defined on a… (More)

Hysteresis effects in two-phase flow in porous media are important in applications such as waterflooding or gas storage in sand aquifers. In this paper, we develop a numerical scheme for such a flow where the permeability hysteresis is modeled by a family of reversible scanning curves enclosed by irreversible imbibition and drainage permeability curves. The… (More)