  The numerical radius of a matrix is a scalar quantity that has many
applications in the study of matrix analysis. Due to the difficulty in
computing the numerical radius, inequalities bounding it have received a
considerable attention in the literature. In this article, we present many new
bounds for the numerical radius of accretive matrices. The importance of this
study is the presence of a new approach that treats a specific class of
matrices, namely the accretive ones. The new bounds provide a new set of
inequalities, some of which can be considered as refinements of other existing
ones, while others present new insight to some known results for positive
matrices.
