  In this paper we study greedy approximation in Banach spaces. We discuss a
modification of the Weak Chebyshev Greedy Algorithm, in which steps of the
algorithm can be executed imprecisely. Such inaccuracies are represented by
both absolute and relative errors, which provides more flexibility for
numerical applications. We obtain the conditions on the error parameters that
guarantee convergence of the algorithm in all uniformly smooth Banach spaces
and prove that these conditions are sharp. Additionally, we discuss the
conditions that need to be imposed on a Banach space to guarantee convergence
of the Chebyshev Greedy Algorithm, and construct a smooth Banach space in which
the algorithm diverges.
