We propose a class of preconditioners for large positive definite linear systems, arising in nonlinear optimization frameworks. These preconditioners can be computed as by‐product of Krylov‐subspace solvers. Preconditioners in our class are chosen by setting the values of some user‐dependent parameters. We first provide some basic spectral properties which motivate a theoretical interest for the proposed class of preconditioners. Then, we report the results of a comparative numerical experience, among some preconditioners in our class, the unpreconditioned case and the preconditioner in Fasano and Roma (Comput Optim Appl 56:253–290, 2013). The experience was carried on first considering some relevant linear systems proposed in the literature. Then, we embedded our preconditioners within a linesearch‐based Truncated Newton method, where sequences of linear systems (namely Newton’s equations), are required to be solved. We performed an extensive numerical testing over the entire medium‐large scale convex unconstrained optimization test set of CUTEst collection (Gould et al. Comput Optim Appl 60:545–557, 2015), confirming the efficiency of our proposal and the improvement with respect to the preconditioner in Fasano and Roma (Comput Optim Appl 56:253–290, 2013).
