  Distributed matrix computations over large clusters can suffer from the
problem of slow or failed worker nodes (called stragglers) which can dominate
the overall job execution time. Coded computation utilizes concepts from
erasure coding to mitigate the effect of stragglers by running 'coded' copies
of tasks comprising a job; stragglers are typically treated as erasures. While
this is useful, there are issues with applying, e.g., MDS codes in a
straightforward manner. Several practical matrix computation scenarios involve
sparse matrices. MDS codes typically require dense linear combinations of
submatrices of the original matrices which destroy their inherent sparsity.
This is problematic as it results in significantly higher worker computation
times. Moreover, treating slow nodes as erasures ignores the potentially useful
partial computations performed by them. Furthermore, some MDS techniques also
suffer from significant numerical stability issues. In this work we present
schemes that allow us to leverage partial computation by stragglers while
imposing constraints on the level of coding that is required in generating the
encoded submatrices. This significantly reduces the worker computation time as
compared to previous approaches and results in improved numerical stability in
the decoding process. Exhaustive numerical experiments on Amazon Web Services
(AWS) clusters support our findings.
