Newton-like Polynomial-Coded Distributed Computing for Numerical Stability

For coded distributed computing (CDC), polynomial code is one prevalent encoding method for CDC (called Poly-CDC). It suffers from poor numerical stability due to the Vandermonde matrix serving as coefficient which needs be inverted, and whose condition number increases exponentially with size of or equivalently parallel worker nodes. To improve stability, especially large networks, we propose a Newton-like (NLPC)-based (NLPC-CDC), design dedicated both matrix–vector matrix–matrix multiplications. The associated proof constructed possesses (n,k)-symmetrical combination property (CP), where symmetrical means nodes have identical computation volume, CP k-symmetrical original tasks are encoded into n(n≥k)-symmetrically tasks, arbitrary k resulting n-coded can recover intended results. Extensive studies verify significant improvement our proposed NLPC-CDC over Poly-CDC.