Numerically Stable Coded Matrix Computations via Circulant and Rotation Matrix Embeddings

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