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A note on regularity and positive definiteness of interval matrices

100%

Farhadsefat R., Lotfi T., Rohn J.

Open Mathematics

2012

tom 10

nr 1

322-328

We present a sufficient regularity condition for interval matrices which generalizes two previously known ones. It is formulated in terms of positive definiteness of a certain point matrix, and can also be used for checking positive definiteness of interval matrices. Comparing it with Beeck’s strong regularity condition, we show by counterexamples that none of the two conditions is more general than the other one.

Complexity issues for the symmetric interval eigenvalue problem

88%

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

2 Open Mathematics

1 Farhadsefat R.

1 Hladík M.

1 Lotfi T.

1 Rohn J.

1 2014

1 2012

Wyniki wyszukiwania

A note on regularity and positive definiteness of interval matrices

Complexity issues for the symmetric interval eigenvalue problem