A random one-dimensional line-search algorithm computes the largest generalized Rayleigh quotient using only matrix-vector products with A and B, without adjoints or B^{-1}, with almost-sure convergence to the global maximizer.
Benzi, Some uses of the field of values in numerical analysis, Boll
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Stochastic Zeroth-Order Method for Computing Generalized Rayleigh Quotients
A random one-dimensional line-search algorithm computes the largest generalized Rayleigh quotient using only matrix-vector products with A and B, without adjoints or B^{-1}, with almost-sure convergence to the global maximizer.