  Two field-sparsening methods, namely the sparse-grid method and the random
field selection method, are used in this paper for the construction of the
2-point and 3-point correlation functions in lattice QCD. We argue that, due to
the high correlation among the lattice correlators at different field points
associated with source, current, and sink locations, one can save a lot of
computational time by performing the summation over a subset of the lattice
sites. Furthermore, with this strategy, one only needs to store a small
fraction of the full quark propagators. It is found that the number of field
points can be reduced by a factor of $\sim$100 for the point-source operator
and a factor of $\sim$1000 for the Gaussian-smeared operator, while the
uncertainties of the correlators only increase by $\sim$15\%. Therefore, with a
modest cost of the computational resources, one can approach the precision of
the all-to-all correlators using the field-sparsening methods.
