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An envelope for the spectrum of a matrix

100%

Psarrakos P., Tsatsomeros M.

Open Mathematics

2012

tom 10

nr 1

292-302

We introduce and study an envelope-type region ɛ(A) in the complex plane that contains the eigenvalues of a given n×n complex matrix A. ɛ(A) is the intersection of an infinite number of regions defined by cubic curves. The notion and method of construction of ɛ(A) extend the notion of the numerical range of A, F(A), which is known to be an intersection of an infinite number of half-planes; as a consequence, ɛ(A) is contained in F(A) and represents an improvement in localizing the spectrum of A.

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 Hladík M.

1 Psarrakos P.

1 Tsatsomeros M.

1 2014

1 2012

Wyniki wyszukiwania

An envelope for the spectrum of a matrix

Complexity issues for the symmetric interval eigenvalue problem