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This work studies limited memory preconditioners for linear symmetric positive definite systems of equations. Connections are established between a partial Cholesky factorization from the literature and a variant of Quasi-Newton type preconditioners. Then, a strategy for enhancing the Quasi-Newton preconditioner via available information is proposed. Numerical experiments show the behaviour of the resulting preconditioner.

On Partial Cholesky Factorization and a Variant of Quasi-Newton Preconditioners for Symmetric Positive Definite Matrices