LOW-RANK ITERATIVE METHODS FOR PROJECTED GENERALIZED LYAPUNOV EQUATIONS TATJANA STYKEL Abstract. We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximat...

Abstract: We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractiona...

In this paper we consider the numerical solution of large-scale projected generalized continuous-time and discrete-time Sylvester equations with low-rank right-hand sides. First, we present the results on the sufficient conditions for the existence, uniqueness, and analytic formula of the solutions of these equations. Second, we review the low-rank alternating direction implicit method and the ...

A hybrid numerical scheme has been presented in this paper for channel flow simulation by coupling one-dimensional and two-dimensional models. Both 1D and 2D differential equations have been discretized by applying the finite volume cell-centered method in a collocated grid system and solved along channel axis for all sections and elements. Due to truncation, dissipation and round off errors, u...

Studies of implicit learning often examine peoples' sensitivity to sequential structure. Computational accounts have evolved to reflect this bias. An experiment conducted by Neil and Higham [Neil, G. J., & Higham, P. A.(2012). Implicit learning of conjunctive rule sets: An alternative to artificial grammars. Consciousness and Cognition, 21, 1393-1400] points to limitations in the sequential app...

We deal with situations incongruent with our automatic response tendencies much better right after having done so on a previous trial than after having reacted to a congruent trial. The nature of the mechanisms responsible for these sequential congruency effects is currently a hot topic of debate. According to the conflict monitoring model these effects depend on the adjustment of control trigg...

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost performance of scientific experiment. Sequential BED, as opposed static considers scenario where we can sequentially update our beliefs about model parameters through data gathered in A class particular interest for natural medical sciences are implicit model...