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Enclosures for the solution set of parametric interval linear systems

Milan Hladík (2012)

International Journal of Applied Mathematics and Computer Science

We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods....

Epsilon-inflation with contractive interval functions

Günter Mayer (1998)

Applications of Mathematics

For contractive interval functions [ g ] we show that [ g ] ( [ x ] ϵ k 0 ) ⊆ ∫ ( [ x ] ϵ k 0 ) results from the iterative process [ x ] k + 1 : = [ g ] ( [ x ] ϵ k ) after finitely many iterations if one uses the epsilon-inflated vector [ x ] ϵ k as input for [ g ] instead of the original output vector [ x ] k . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.

Error autocorrection in rational approximation and interval estimates. [A survey of results.]

Grigori Litvinov (2003)

Open Mathematics

The error autocorrection effect means that in a calculation all the intermediate errors compensate each other, so the final result is much more accurate than the intermediate results. In this case standard interval estimates (in the framework of interval analysis including the so-called a posteriori interval analysis of Yu. Matijasevich) are too pessimistic. We shall discuss a very strong form of the effect which appears in rational approximations to functions. The error autocorrection effect occurs...

Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control

Jarosław Smoczek (2013)

International Journal of Applied Mathematics and Computer Science

A hybrid method combining an evolutionary search strategy, interval mathematics and pole assignment-based closed-loop control synthesis is proposed to design a robust TSK fuzzy controller. The design objective is to minimize the number of linear controllers associated with rule conclusions and tune the triangular-shaped membership function parameters of a fuzzy controller to satisfy stability and desired dynamic performances in the presence of system parameter variation. The robust performance objective...

Extending the applicability of Newton's method using nondiscrete induction

Ioannis K. Argyros, Saïd Hilout (2013)

Czechoslovak Mathematical Journal

We extend the applicability of Newton's method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Pták. We obtain new sufficient convergence conditions for Newton's method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F. A. Potra, V. Pták, Sharp error bounds for Newton's process, Numer. Math., 34 (1980), 63–72, and F. A. Potra, V. Pták, Nondiscrete...

Fast and correctly rounded logarithms in double-precision

Florent de Dinechin, Christoph Lauter, Jean-Michel Muller (2007)

RAIRO - Theoretical Informatics and Applications

This article is a case study in the implementation of a portable, proven and efficient correctly rounded elementary function in double-precision. We describe the methodology used to achieve these goals in the crlibm library. There are two novel aspects to this approach. The first is the proof framework, and in general the techniques used to balance performance and provability. The second is the introduction of processor-specific optimization to get performance equivalent to the best current...

Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies

Vicenç Puig (2010)

International Journal of Applied Mathematics and Computer Science

This paper reviews the use of set-membership methods in fault diagnosis (FD) and fault tolerant control (FTC). Setmembership methods use a deterministic unknown-but-bounded description of noise and parametric uncertainty (interval models). These methods aims at checking the consistency between observed and predicted behaviour by using simple sets to approximate the exact set of possible behaviour (in the parameter or the state space). When an inconsistency is detected between the measured and predicted...

Formally certified floating-point filters for homogeneous geometric predicates

Guillaume Melquiond, Sylvain Pion (2007)

RAIRO - Theoretical Informatics and Applications

Floating-point arithmetic provides a fast but inexact way of computing geometric predicates. In order for these predicates to be exact, it is important to rule out all the numerical situations where floating-point computations could lead to wrong results. Taking into account all the potential problems is a tedious work to do by hand. We study in this paper a floating-point implementation of a filter for the orientation-2 predicate, and how a formal and partially automatized verification of this...

Currently displaying 61 – 80 of 177