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- Milan Hladík
- Applied Mathematics and Computer Science
- 2012

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… (More)

- Milan Hladík, David Daney, Elias P. Tsigaridas
- SIAM J. Matrix Analysis Applications
- 2010

We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce as-sharp-as-possible bounds. We consider two cases: general and symmetric interval matrices. We focus on the latter case, since on one hand such interval matrices have many applications in mechanics and engineering, and on the other many… (More)

- Milan Hladík
- SIAM J. Matrix Analysis Applications
- 2008

- Milan Hladík, David Daney, Elias P. Tsigaridas
- Computers & Mathematics with Applications
- 2011

We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner approximation algorithm, that in many case estimates exact bounds. To our knowledge, this is the first algorithm that is… (More)

- Milan Hladík, Elias P. Tsigaridas, Milan Hlad́ık, David Daney
- 2009

We study bounds on eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce as-sharp-as-possible bounds. We consider two cases: general (unsymmetric) and symmetric interval matrices. We focus on the latter case, since on one hand these such interval matrices have many applications in mechanics and engineering, and on… (More)

- Milan Hladík
- FO & DM
- 2009

- Milan Hladík
- Optimization Methods and Software
- 2008

- Milan Hladík, David Daney, Elias P. Tsigaridas
- Applied Mathematics and Computation
- 2011

We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer estimation of the real eigenvalue set of an interval matrix, we propose a filtering method that improves the estimation. Even though our method is based on an sufficient regularity condition, it is very efficient in practice, and our… (More)

- Milan Hladík
- European Journal of Operational Research
- 2010

This paper reflects the renascence of sensitivity and parametric analysis in linear programming and extends single-parametric results to the case when there are multiple parameters in the objective function and in the right-hand side of equations. Multiparametric approach enables us to study more complex perturbation occurring in linear programs than the… (More)