  This article presents a novel numerically tractable technique for
synthesizing Lyapunov functions for equilibria of nonlinear vector fields. In
broad strokes, corresponding to an isolated equilibrium point of a given vector
field, a selection is made of a compact neighborhood of the equilibrium and a
dictionary of functions in which a Lyapunov function is expected to lie. Then
an algorithmic procedure based on the recent work [DACC22] is deployed on the
preceding neighborhood-dictionary pair and charged with the task of finding a
function satisfying a compact family of inequalities that defines the behavior
of a Lyapunov function on the selected neighborhood. The technique applies to
continuous nonlinear vector fields without special algebraic structures and
does not even require their analytical expressions to proceed. Several
numerical examples are presented to illustrate our results.
