Nearly defective complex eigenvalues in Bessel matrices (Q1124926)

The behavior of eigenvalues of \(n\times n\) Bessel matrices \(T_n\) is studied. The problem of computing the eigenvalues using finite precision brings difficulties. The computation of the distance from \(T_n\) to the nearest defective matrix is tackled using two approaches. The first approach provides an estimation of the distance from \(T_n\) to the nearest defective matrix with an imposed multiple eigenvalue, the second looks for the closest defective matrix with any multiple eigenvalue (the second approach is of statistical type). The second approach provides a sharper estimation of the distance to the nearest defective matrix. The reason of appearance of a numerical instability for \(n\geq 23\) is discussed.