All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 177

Showing per page

Complexity of computing interval matrix powers for special classes of matrices

David Hartman, Milan Hladík (2020)

Applications of Mathematics

Computing powers of interval matrices is a computationally hard problem. Indeed, it is NP-hard even when the exponent is 3 and the matrices only have interval components in one row and one column. Motivated by this result, we consider special types of interval matrices where the interval components occupy specific positions. We show that computing the third power of matrices with only one column occupied by interval components can be solved in cubic time; so the asymptotic time complexity is the...

Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method

François Alouges (2001)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching the decay...

Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method

François Alouges (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching the...

Computing and Visualizing Solution Sets of Interval Linear Systems

Krämer, Walter (2007)

Serdica Journal of Computing

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006The computation of the exact solution set of an interval linear system is a nontrivial task [2, 13]. Even in two and three dimensions a lot of work has to be done. We demonstrate two different realizations. The first approach (see [16]) is based on Java, Java3D, and the BigRational package [21]. An applet allows modifications of the matrix coefficients and/or the coefficients...

Computing discrete convolutions with verified accuracy via Banach algebras and the FFT

Jean-Philippe Lessard (2018)

Applications of Mathematics

We introduce a method to compute rigorous component-wise enclosures of discrete convolutions using the fast Fourier transform, the properties of Banach algebras, and interval arithmetic. The purpose of this new approach is to improve the implementation and the applicability of computer-assisted proofs performed in weighed ℓ 1 Banach algebras of Fourier/Chebyshev sequences, whose norms are known to be numerically unstable. We introduce some application examples, in particular a rigorous aposteriori...

Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets: a modal interval analysis approach

Jian Wan, Josep Vehí, Ningsu Luo, Pau Herrero (2009)

ESAIM: Control, Optimisation and Calculus of Variations

A general framework for computing robust controllable sets of constrained nonlinear uncertain discrete-time systems as well as controlling such complex systems based on the computed robust controllable sets is introduced in this paper. The addressed one-step control approach turns out to be a robust model predictive control scheme with feasible unit control horizon and contractive constraint. The solver of 1-dimensional quantified set inversion in modal interval analysis is extended to 2-dimensional...

Convergence conditions for Secant-type methods

Ioannis K. Argyros, Said Hilout (2010)

Czechoslovak Mathematical Journal

We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions...

Correct rounding of algebraic functions

Nicolas Brisebarre, Jean-Michel Muller (2007)

RAIRO - Theoretical Informatics and Applications

We explicit the link between the computer arithmetic problem of providing correctly rounded algebraic functions and some diophantine approximation issues. This allows to get bounds on the accuracy with which intermediate calculations must be performed to correctly round these functions.

Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems

Mareile Freihold, Eberhard P. Hofer (2009)

International Journal of Applied Mathematics and Computer Science

Interval arithmetic techniques such as VALENCIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for...

Deterministic global optimization using interval constraint propagation techniques

Frederic Messine (2004)

RAIRO - Operations Research - Recherche Opérationnelle

The purpose of this article is to show the great interest of the use of propagation (or pruning) techniques, inside classical interval Branch-and-Bound algorithms. Therefore, a propagation technique based on the construction of the calculus tree is entirely explained and some properties are presented without the need of any formalism (excepted interval analysis). This approach is then validated on a real example: the optimal design of an electrical rotating machine.

Deterministic global optimization using interval constraint propagation techniques

Frederic Messine (2010)

RAIRO - Operations Research

The purpose of this article is to show the great interest of the use of propagation (or pruning) techniques, inside classical interval Branch-and-Bound algorithms. Therefore, a propagation technique based on the construction of the calculus tree is entirely explained and some properties are presented without the need of any formalism (excepted interval analysis). This approach is then validated on a real example: the optimal design of an electrical rotating machine.

Directed forests with application to algorithms related to Markov chains

Piotr Pokarowski (1999)

Applicationes Mathematicae

This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.

Ein effizienter Algorithmus zur iterativen Einschliessung der inversen Matrix

Jürgen Herzberger (1987)

Aplikace matematiky

Es wird ein kombinierter Algorithmus zur iterativen Einschlissung der Inversen einer Matrix beschrieben. Es handelt sich dabei um eine intervallmässige Version des Schulz'schen Verfahrens. Es wird bewiesen, dass der Algorithmus genauso effizient ist wie ein hisher bekannter aus [2], dass er aber in Bezug auf den akkumulierten Rundungsfehler dem bisherigen Vorgehen vorzuziehen ist. Ein numerisches Beispiel wird gegeben.

Currently displaying 41 – 60 of 177