Componentwise Distance to Singularity
Дата
Авторы
Rex,G.
Journal Title
Journal ISSN
Volume Title
Издатель
Journal of Universal Computer Science
Аннотация
Описание
A perturbation matrix is considered, where and . The matrix is singular iff contains a real singular matrix. A problem is to decide if is singular or nonsingular, a NP-hard problem. The decision can be made by the computation of the componentwise distance to the nearest singular matrix defined on the basis of the real spectral radius, and by the solution of 4n eigenvalue problems. Theorem 6 gives a new computation basis, a natural way to the "componentwise distance ..." definition, and a motivation to rename this in radius of singularity denoted by sir . This new way shows: (i) - sir results from a real nonnegative eigensolution of a non-linear mapping, (ii) - sir has a norm representation, (iii) - sir can be computed by 2n-1 nonnegative eigensolutions of the nonlinear mapping, (iv) - for the special case a formula for a computation of sir is given, also a trivial algorithm for the computation, and some examples as demonstration.
Ключевые слова
perturbation matrix , interval matrix , componentwise distance to the nearest singular matrix , radius of singularity , NP-hard