The spectrum of a modified linear pencil (Q597277)

In Section 2 of this paper, the authors derive the secular equation. In Section 3, they describe the divide and conquer method which exploits the secular equation of Section 2 to efficiently compute the eigenvalues of a symmetric tridiagonal pair. In Section 4, they derive a second-order method for computing the zeros of the secular equation which was presented in Section 2. In Section 5.1, they illustrate the method on a small matrix tearing problem and in Section 5.2 they report on some numerical tests. Finally, in Section 6, they draw some conclusions regarding this work.