In this paper we present a method, parallel in nature, for finding all eigenvalues of a symmetric generalized tridiagonal matrix. Our method employs the determinant evaluation and the Durand-Kerner root-finding scheme. It will be shown that the method converges quadratically and is reliable, efficient, and easy to implement in practice.
"Durand-Kerner Root-Finding Method for the Generalized Tridiagonal Eigenproblem." Missouri J. Math. Sci. 11 (1) 33 - 43, Winter 1999. https://doi.org/10.35834/1999/1101033