Recent results on the Grassmannian perspective of soliton equations with an elliptic spectral parameter are presented along with a detailed review of the classical case with a rational spectral parameter. The nonlinear Schrödinger hierarchy is picked out for illustration of the classical case. This system is formulated as a dynamical system on a Lie group of Laurent series with factorization st...

We study the basic notions related to the stabilization of an infinite-dimensional well-posed linear system in the sense of Salamon and Weiss. We first introduce an appropriate stabilizability and detectability notion, and show that if a system is jointly stabilizable and detectable then its transfer function has a doubly coprime factorization in Hm. The converse is also true: every function wi...

The standard way to obtain explicit formulas for spectral factorization problems for rational transfer functions is to use a minimal realization and then obtain formulae in terms of the generators A, B, C and D. For well-posed linear systems with unbounded generators these formulae will not always be well-defined. Instead, we suggest another approach for the class of well-posed linear systems f...

Lower/Upper triangular (LU) factorization plays an important role in scientific and high performance computing. This paper presents an implementation of the LU decomposition algorithm for double precision complex numbers on a star topology based multi-FPGA platform. The out of core implementation moves data through multiple levels of a hierarchical memory system (hard disk, DDR SDRAMs and FPGA ...

A major element of codesign is the task of decomposing a design in order to target some of its components to hardware and some to software while maintaining the integrity of the execution model. We illustrate how a previously developed algebraic technique we call system factorization adapts to this notion of decomposition. As an example, we describe how the mechanization of system factorization...

Uncertainties are unavoidable in practical situations and they have to be taken into consideration in control system design. In this paper, a method for designing a robust observer for linear time-delay systems is proposed. Under the assumption that the considered time-delay system is spectrally controllable and spectrally observable, a double Bézout factorization of its nominal transfer matrix...

Recent results on the Grassmannian perspective of soliton equations with an elliptic spectral parameter are presented along with a detailed review of the classical case with a rational spectral parameter. The nonlinear Schrödinger hierarchy is picked out for illustration of the classical case. This system is formulated as a dynamical system on a Lie group of Laurent series with factorization st...

This article studies the effect of discretization order on preconditioning and convergence of a high-order Newton–Krylov unstructured flow solver. The generalized minimal residual (GMRES) algorithm is used for inexactly solving the linear system arising from implicit time discretization of the governing equations. A first-order Jacobian is used as the preconditioning matrix. The complete lower–...

Recent results on the Grassmannian perspective of soliton equations with an elliptic spectral parameter are presented along with a detailed review of the classical case with a rational spectral parameter. The nonlinear Schrödinger hierarchy is picked out for illustration of the classical case. This system is formulated as a dynamical system on a Lie group of Laurent series with factorization st...

This paper proposes a direct solver for symmetric indefinite linear systems. The program is parallelized via the OpenMP task construct and outperforms existing programs. proposed avoids pivoting, which requires lot of data movement, during factorization with preconditioning using random butterfly transformation. matrix layout tiled after to more efficiently use cache memory factorization. Given...