On Kublanovskaya’s Approach to the Solution of the Generalized Latent Value Problem for Functional $\lambda $-Matrices

Abstract

In SIAM J. Numer. Anal., 7 (1970), pp. 532–537, Kublanovskaya proposed a quadratically convergent algorithm for computing the eigenvalues of the generalized latent value problem for $\lambda $-matrices. In this contribution we show that Kublanovskaya’s algorithm does not constitute a Newton iteration, though it can be justified through its equivalence with the generalized Rayleigh quotient. An alternative iteration scheme that can provide a higher order of convergence is proposed.