  Polynomial based methods have recently been used in several works for
mitigating the effect of stragglers (slow or failed nodes) in distributed
matrix computations. For a system with $n$ worker nodes where $s$ can be
stragglers, these approaches allow for an optimal recovery threshold, whereby
the intended result can be decoded as long as any $(n-s)$ worker nodes complete
their tasks. However, they suffer from serious numerical issues owing to the
condition number of the corresponding real Vandermonde-structured recovery
matrices; this condition number grows exponentially in $n$. We present a novel
approach that leverages the properties of circulant permutation matrices and
rotation matrices for coded matrix computation. In addition to having an
optimal recovery threshold, we demonstrate an upper bound on the worst-case
condition number of our recovery matrices which grows as $\approx
O(n^{s+5.5})$; in the practical scenario where $s$ is a constant, this grows
polynomially in $n$. Our schemes leverage the well-behaved conditioning of
complex Vandermonde matrices with parameters on the complex unit circle, while
still working with computation over the reals. Exhaustive experimental results
demonstrate that our proposed method has condition numbers that are orders of
magnitude lower than prior work.
