Related papers: A Note on the Reduction Formulas for Some Systems …
A common computational approach for polynomial optimization problems (POPs) is to use (hierarchies of) semidefinite programming (SDP) relaxations. When the variables in the POP are required to be nonnegative, these SDP problems typically…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely…
A Lyapunov matrix equation can be converted, by using the Jordan decomposition theorem for matrices, into an equivalent Lyapunov matrix equation where the matrix is a Jordan matrix. The Lyapunov matrix equation with Jordan matrix can be…
We give a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces in terms of direct integrals. Precisely, we study the uniqueness of strongly irreducible…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three…
In this paper we discuss the notion of reducibility for matrix weights and introduce a real vector space $\mathcal C_\mathbb{R}$ which encodes all information about the reducibility of $W$. In particular a weight $W$ reduces if and only if…
A nonhomogeneous system of linear recurrence equations can be recognized by an automaton $\mathcal{A}$ over a one-letter alphabet $A = \{z\}$. Conversely, the automaton $\mathcal{A}$ generates precisely this nonhomogeneous system of linear…
We present order reduction results for linear time invariant descriptor systems. Results are given for both forced and unforced systems as well methods for constructing the reduced order systems. Our results establish a precise connection…
We study the reduction in a lambda-calculus derived from Moggi's computational one, that we call the computational core. The reduction relation consists of rules obtained by orienting three monadic laws. Such laws, in particular…
The construction of the general solution sequence of row-finite linear systems is accomplished by implementing -ad infinitum- the Gauss-Jordan algorithm under a rightmost pivot elimination strategy. The algorithm generates a basis (finite…
Systems may depend on parameters which one may control, or which serve to optimise the system, or are imposed externally, or they could be uncertain. This last case is taken as the ``Leitmotiv'' for the following. A reduced order model is…
Model order reduction is the approximation of dynamical systems into equivalent systems with smaller order. Model reduction has been studied extensively for different types of systems. In this paper, we present two methods for multi input…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…
Two comprehensive approaches are considered for constructing projection-based reduced-order computational models for linear dynamical systems. The first one reduces the governing equations written in the descriptor form, using a Galerkin or…