  This work introduces a method for determining the energy spectrum of lattice
quantum chromodynamics (LQCD) by applying the Lanczos algorithm to the transfer
matrix. Proof-of-principle analyses of the simple harmonic oscillator and the
LQCD proton mass demonstrate that this method provides faster ground-state
convergence than standard energy estimators, which are related to the
power-iteration algorithm. Lanczos provides more accurate energy estimates than
multi-state fits to correlation functions with small imaginary times while
achieving comparable statistical precision. Two-sided error bounds are computed
for Lanczos results and guarantee that excited-state effects cannot shift
Lanczos results far outside their statistical uncertainties. Further, Lanczos
results avoid the exponential signal-to-noise degradation present in standard
energy estimators.
