Verified real eigenvector of an interval matrix.
For a square interval matrix A and a real vector x, this function verifies x to be an eigenvector of some matrix in A, or not to be an eigenvector of any matrix in A, or yields no verified result (unfortunately, complex eigenvectors cannot be handled yet):
x is verified to be an eigenvector of some matrix in A, lambda is an interval number such that for each lambda0 ∈ lambda, A is verified to contain a matrix having (lamda0, x) as an eigenpair, As is a very tight interval matrix verified to contain a matrix having (mid (lambda), x) as an eigenpair,
x is verified not to be an eigenvector of any matrix in A, lambda and As consist of empty intervals,
no verified result (data may be wrong).
Based on the section “Real eigenvectors” in J. Rohn, A handbook of results on interval linear problems, posted at http://www.cs.cas.cz/~rohn.
This work was supported by the Czech Republic National Research Program “Information Society”, project 1ET400300415.
See also: eig.
Package: interval