Related papers: Computing Enclosures of Overdetermined Interval Li…
Presented is a new method yielding parameterized solution to an interval parametric linear system. Some properties of this method are discussed. The solution enclosure it provides is compared to the enclosures by other methods. It is shown…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
In this paper, we consider the solution of ill-conditioned systems of linear algebraic equations that can be determined imprecisely. To improve the stability of the solution process, we "immerse" the original imprecise linear system in an…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
This paper presents a novel set-based computing method, called interval superposition arithmetic, for enclosing the image set of multivariate factorable functions on a given domain. In order to construct such enclosures, the proposed…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the nonlinear dynamics into a higher dimensional linear model. In particular, we focus on the \emph{maximal admissible…
Quantifying extra functions, herein referred to as outcome functions, over optimal solutions of an optimization problem can provide decision makers with additional information on a system. This bears more importance when the optimization…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…
In this paper, we first propose a method that can efficiently compute the maximal robust controlled invariant set for discrete-time linear systems with pure delay in input. The key to this method is to construct an auxiliary linear system…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
The authors proposed a general way to find particular solutions for overdetermined systems of PDEs previously, where the number of equations is greater than the number of unknown functions. In this paper, we propose an algorithm for finding…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…