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Polynomial based methods have recently been used in several works formitigating the effect of stragglers (slow or failed nodes) in distributedmatrix computations. For a system with $n$ worker nodes where $s$ can bestragglers, these approaches allow for an optimal recovery threshold, wherebythe intended result can be decoded as long as any $(n-s)$ worker nodes completetheir tasks. However, they suffer from serious numerical issues owing to thecondition number of the corresponding real Vandermonde-structured recoverymatrices; this condition number grows exponentially in $n$. We present a novelapproach that leverages the properties of circulant permutation matrices androtation matrices for coded matrix computation. In addition to having anoptimal recovery threshold, we demonstrate an upper bound on the worst-casecondition number of our recovery matrices which grows as $\approxO(n^{s+5.5})$; in the practical scenario where $s$ is a constant, this growspolynomially in $n$. Our schemes leverage the well-behaved conditioning ofcomplex Vandermonde matrices with parameters on the complex unit circle, whilestill working with computation over the reals. Exhaustive experimental resultsdemonstrate that our proposed method has condition numbers that are orders ofmagnitude lower than prior work.

Numerically stable coded matrix computations via circulant and rotation matrix embeddings