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Enclosures for the solution set of parametric interval linear systems

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Hladík M.

International Journal of Applied Mathematics and Computer Science

2012

tom 22

nr 3

561-574

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.

Complexity issues for the symmetric interval eigenvalue problem

100%

Hladík M.

Open Mathematics

2015

tom 13

nr 1

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. We show in which error factors the problem is polynomially solvable and in which factors it becomes NP-hard.

Ograniczanie wyników

1 International Journal of Applied Mathematics and Computer Science

1 Open Mathematics

2 Hladík M.

1 2014

1 2012

Wyniki wyszukiwania

Enclosures for the solution set of parametric interval linear systems

Complexity issues for the symmetric interval eigenvalue problem