Numerical approximation of the product of the square root of a matrix with a vector

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A black-box rational Arnoldi variant for Cauchy–Stieltjes matrix functions (2013, methodology): “Functions of this type also arise in the context of computation of Neumann-to-Dirichlet and Dirichlet-to-Neumann maps [16, 3], the solution of systems of stochastic differential equations [2], and in quantum chromodynamics [22].”
The extended Krylov subspace method and orthogonal Laurent polynomials (2009, background): “An early discussion on the approximation of large-scale expressions of the form (1.1) is presented by van der Vorst [26]; see also [27, Chapter 11].”