An Implementation of Vincent's Theorem.
An improved convergence analysis of a superquadratic method for solving generalized equations.
An Interval Arithmetic Algorithm for Multivariate Constrained Global Optimization Using Cord-Slope Forms of Taylor's Expansion
An interval method for nonlinear systems of equations
An iterative algorithm for testing solvability of max-min interval systems
This paper is dealing with solvability of interval systems of linear equations in max-min algebra. Max-min algebra is the algebraic structure in which classical addition and multiplication are replaced by and , where . The notation represents an interval system of linear equations, where and are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 and T5 solvability and give necessary and...
Analytic enclosure of the fundamental matrix solution
This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained by computing...
Ansätze für einen intervallmathematischen bzw. logisch dreiwertigen Aufbau der analytischen Geometrie
Anwendungen des Fixpunktsatzes für Pseudometrische Räume in der Intervallrechnung.
Application de l'optimisation en nombres entiers à un problème d'«arrondissage»
Application of interval arithmetic in the evaluation of transfer capabilities by considering the sources of uncertainty.
Ausgleichs-Klassenkegelschnitte
Auswertungsverfahren für Polynome in mehreren Variablen.
Average errors for zero finding: lower bounds for smooth or monotone functions.
Backward Error Analysis for Totally Positive Linear Systems.
Bemerkungen zum Verfahren der koordinatenweisen Suche
In der vorliegenden Arbeit wird das Verfahren der koordinatenweisen Suche mit Hilfe der Intervallarithmetik realisiert. Dadurch ist es möglich, bei speziellen nichtlinearen Optimierungsproblemen alle auftretenden Fehlerarten zu erfaßen, einschliesslich eingangsbedingter Fehler. Vor- und Nachteile werden erläutert sowie Testbeispiele angegeben.
Berechnung des charakteristischen Exponenten der endlichen Hillschen Differentialgleichung durch Numerische Integration.
Bounding the maximum value of the real-valued sequence.
Brèves communications. Étude de l'erreur d'arrondi dans la résolution de systèmes linéaires par des méthodes itératives
Checking positive definiteness or stability of symmetric interval matrices is NP-hard
It is proved that checking positive definiteness, stability or nonsingularity of all [symmetric] matrices contained in a symmetric interval matrix is NP-hard.
Complexity issues for the symmetric interval eigenvalue problem
We study the problem of computing the maximal and minimal possible eigenvalues of a symmetric matrix when the matrix entries vary within compact intervals. In particular, we focus on computational complexity of determining these extremal eigenvalues with some approximation error. Besides the classical absolute and relative approximation errors, which turn out not to be suitable for this problem, we adapt a less known one related to the relative error, and also propose a novel approximation error....