where λ are the eigenvalues estimated from an approximate basis set χ and λ are the true eigenvalues. The sum runs over the first k eigenvalues, which are typically the dominant slow relaxation processes that one is interested in approximating; while r is some arbitrary positive integer. When r = 1 and the model is assumed to be stationary, the left-hand side of Equation is known as the Generalized Matrix Rayleigh Quotient (GMRQ):