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Enclosures for the solution set of parametric interval linear systems

100%

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.

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Intervals of certain classes of Z-matrices

88%

Kannan M., Sivakumar K.

Discussiones Mathematicae - General Algebra and Applications

2014

tom 34

nr 1

85-93

Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 International Journal of Applied Mathematics and Computer Science

1 Hladík M.

1 Kannan M.

1 Sivakumar K.

1 2014

1 2012

Wyniki wyszukiwania

Enclosures for the solution set of parametric interval linear systems

Intervals of certain classes of Z-matrices