From the theorem of Ważewski to computer assisted proofs in dynamics
Global Optimization Using Interval Analysis - The Multi-Dimensional Case.
Improved local convergence analysis of inexact Newton-like methods under the majorant condition
We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations. Using more precise majorant conditions than in earlier studies, we provide: a larger radius of convergence; tighter error estimates on the distances involved; and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.
Improving the efficiency of exclusion algorithms.
Interval algorithm for absolute value equations
We investigate the absolute value equations Ax−|x| = b. Based on ɛ-inflation, an interval verification method is proposed. Theoretic analysis and numerical results show that the new proposed method is effective.
Interval analysis for certified numerical solution of problems in robotics
Interval analysis is a relatively new mathematical tool that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization, but numerous other problems may be addressed as well. This approach has the following general advantages: (a) it allows to find solutions of a problem only within some finite domain which make sense as soon as the unknowns in the problem are physical parameters; (b) numerical computer...
Interval fuzzy matrix equations
This paper deals with the solvability of interval matrix equations in fuzzy algebra. Fuzzy algebra is the algebraic structure in which the classical addition and multiplication are replaced by maximum and minimum, respectively. The notation , where are given interval matrices and is an unknown matrix, represents an interval system of matrix equations. We can define several types of solvability of interval fuzzy matrix equations. In this paper, we shall deal with four of them. We define the...
Interval linear regression analysis based on Minkowski difference – a bridge between traditional and interval linear regression models
In this paper, we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model, the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval...
Interval matrices with Monge property
We generalize the Monge property of real matrices for interval matrices. We define two classes of interval matrices with the Monge property---in a strong and a weak sense. We study the fundamental properties of both types. We show several different characterizations of the strong Monge property. For the weak Monge property, we give a polynomial description and several sufficient and necessary conditions. For both classes, we study closure properties. We further propose a generalization of an algorithm...
Interval solutions of linear interval equations
It is shown that if the concept of an interval solution to a system of linear interval equations given by Ratschek and Sauer is slightly modified, then only two nonlinear equations are to be solved to find a modified interval solution or to verify that no such solution exists.
Intervallarithmetik - mit Zirkel und Lineal.
Inverse interval matrix: a survey.
Laguerre-Like Methods for the Simultaneous Approximation of Polynomial Multiple Zeros
Laguerre-like methods with corrections for the inclusion of polynomial zeros.
Level sets of uniform quotient mappings from Rn to R do not need to be locally connected.
We give an example of a uniform quotient map from R2 to R which has non-locally connected level sets.
Lie groups and error analysis.
Linear-quadratic optimal control for the Oseen equations with stabilized finite elements
For robust discretizations of the Navier-Stokes equations with small viscosity, standard Galerkin schemes have to be augmented by stabilization terms due to the indefinite convective terms and due to a possible lost of a discrete inf-sup condition. For optimal control problems for fluids such stabilization have in general an undesired effect in the sense that optimization and discretization do not commute. This is the case for the combination of streamline upwind Petrov-Galerkin (SUPG) and pressure...
L'inverse d'une matrice d'intervalles
Local convergence analysis for a certain class of inexact methods.
Local convergence for the curve tracing of the homotopy method.