  Numerical linked-cluster expansions allow one to calculate finite-temperature
properties of quantum lattice models directly in the thermodynamic limit
through exact solutions of small clusters. However, full diagonalization is
often the limiting factor for these calculations. Here, we show that a partial
diagonalization of the largest clusters in the expansion using the Lanczos
algorithm can be as useful as full diagonalization for the method while
mitigating some of the time and memory issues. As a test case, we consider a
frustrated Heisenberg model on the checkerboard lattice and find that our
approach can lead to much more efficient calculations in a parallel
environment.
