  Polynomial based approaches, such as the Mat-Dot and entangled polynomial
codes (EPC) have been used extensively within coded matrix computations to
obtain schemes with good recovery thresholds. However, these schemes are
well-recognized to suffer from poor numerical stability in decoding. Moreover,
the encoding process in these schemes involves linearly combining a large
number of input submatrices, i.e., the encoding weight is high. For the
practically relevant case of sparse input matrices, this can have the
undesirable effect of significantly increasing the worker node computation
time.
  In this work, we propose a generalization of the EPC scheme by combining the
idea of gradient coding along with the basic EPC encoding. Our technique allows
us to reduce the weight of the encoding and arrive at schemes that exhibit much
better numerical stability; this is achieved at the expense of a worse
threshold. By appropriately setting parameters in our scheme, we recover
several well-known schemes in the literature. Simulation results show that our
scheme provides excellent numerical stability and fast computation speed (for
sparse input matrices) as compared to EPC and Mat-Dot codes.
