Related papers: A Lohner-type algorithm for control systems and or…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
We analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs from Buchmann's, who proved a complexity bound of L(1/2,O(1))…
We introduce and analyze a family of heterogeneous multiscale methods for the numerical integration of highly oscillatory systems of delay differential equations with constant delays. The methodology suggested provides algorithms of…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
We present an algorithm for computing the set of torsion points satisfying a given system of multivariate polynomial equations. Its complexity is quasilinear in the logarithm of the degree of the input equations and exponential in their…
We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an…
We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
We present an efficient algorithm to compute the induced norms of finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both induced $\mathcal{L}_2$ and terminal Euclidean norm penalties. Existing computational…
Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…
We examine numerical rounding errors of some deterministic solvers for systems of ordinary differential equations (ODEs). We show that the accumulation of rounding errors results in a solution that is inherently random and we obtain the…
The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output…
Algorithmic approach to the problem of linearization by point transformation of ordinary differential equation of arbitrary order is presented. Test-linearization is purely algorithmic.