Preconditioning for solving Hermite collocation by the Bi-CGSTABPreconditioning for solving Hermite collocation by the Bi-CGSTAB Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-292006enExplicit pre/post conditioning of the large, sparse and non-symmetric system of equations, arising from the discretization of the Dirichlet Poisson’s Boundary Value Problem (BVP) by the Hermite Collocation method is the problem considered herein. Using the 2-cyclic (red-black) structure of the Collocation coefficient matrix, we investigate the eigenvalue distribution of its preconditioned analogs emerging from its red-black USSOR (UnSymmet- ric SOR) splittings. This analysis, coupled with computational efficiency issues, enables us to justify the choice of Gauss-Seidel (GS) preconditioned schemes as efficient and practical ones, when they used to accelerate the rate of convergence of the Bi-CGSTAB iterative Krylov subspace method. Our results are verified by numerical experiments.http://creativecommons.org/licenses/by/4.0/ACM Transactions on Mathematical Software57811-816 Mathioudakis Emmanouil Μαθιουδακης Εμμανουηλ Saridakis Ioannis Σαριδακης Ιωαννης Papadopoulou Eleni Παπαδοπουλου Ελενη Computing