Related papers: On Parametric Linear System Solving
We present a method for computing all the symmetries of a rational ruled surface defined by a rational parametrization which works directly in parametric rational form, i.e. without computing or making use of the implicit equation of the…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
Superposition of sigmoid function over a finite time interval is shown to be equivalent to the linear combination of the solutions of a linearly parameterized system of logistic differential equations. Due to the linearity with respect to…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…
Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian…
Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this…
In this paper, we study transfer functions corresponding to parametric linear systems whose coefficients are block matrices. Thus, these transfer functions constitute Laurent polynomials whose coefficients are square matrices. We assume…
Many authors studied numeric algorithms for solving the linear systems of the pentadiagonal type. The well-known Fast Pentadiagonal System Solver algorithm is an example of such algorithms. The current article are described new numeric and…
We introduce the parametric matroid one-interdiction problem. Given a matroid, each element of its ground set is associated with a weight that depends linearly on a real parameter from a given parameter interval. The goal is to find, for…
We present a new method for solving symbolically zero--dimensional polynomial equation systems in the affine and toric case. The main feature of our method is the use of problem adapted data structures: arithmetic networks and…
Solving multiple parametrised related systems is an essential component of many numerical tasks, and learning from the already solved systems will make this process faster. In this work, we propose a novel probabilistic linear solver over…
We give a specific method to solve with quadratic complexity the linear systems arising in known algorithms to deal with the sign determination problem. In particular, this enable us to improve the complexity bound for sign determination in…
We present a polynomial-time algorithm that obtains a set of Asymptotic Linear Programs (ALPs) from a given linear system S, such that one of these ALPs admits a feasible solution if and only if S admits a feasible solution. We also show…
We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our…
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…
This paper focuses on representing the $L^{\infty}$-norm of finite-dimensional linear time-invariant systems with parameter-dependent coefficients. Previous studies tackled the problem in a non-parametric scenario by simplifying it to…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…
The work is devoted to the construction of the asymptotic behavior of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends…
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…