Fastest Quotient Iteration for Generalized Self-Adjoint Eigenvalue Problems

Abstract For the generalized eigenvalue problem, a quotient function is devised for estimating eigenvalues in terms of an approximate eigenvector. This gives rise to an infinite family of quotients, a disc centered at the Rayleigh quotient, all entirely arguable to be used in estimation. Although the Rayleigh quotient is among them, one can suggest using it only in an auxiliary manner to choose the quotient in a more optimal way. In normal eigenvalue problems, for any approximate eigenvector, th