Blondel, Vincent
[UCL]
Ninove, Laure
[UCL]
Van Dooren, Paul
[UCL]
In this paper, we consider the conditional affine eigenvalue problem
lambda x = Ax + b, lambda is an element of R, x >= 0, parallel to x parallel to = 1,
where A is an n x n nonnegative matrix, b a nonnegative vector, and parallel to center dot parallel to a monotone vector norm. Under suitable hypotheses, we prove the existence and uniqueness of the solution (lambda(*), x(*)) and give its expression as the Perron root and vector of a matrix A + bc(*)(T) where c(*) has a maximizing property depending on the considered norm. The equation x (Ax + b)/ parallel to Ax + b parallel to has then a unique nonnegative solution, given by the unique Perron vector of A + bc(*)(T). (c) 2005 Elsevier Inc. All rights reserved.
Bibliographic reference |
Blondel, Vincent ; Ninove, Laure ; Van Dooren, Paul. An affine eigenvalue problem on the nonnegative orthant. In: Linear Algebra and Its Applications, Vol. 404, p. 69-84 (2005) |
Permanent URL |
http://hdl.handle.net/2078.1/39245 |