Numerically Stable Polynomially Coded Computing

We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class techniques for providing straggler and fault tolerance in area coded computing. Our contributions are as follows: 1)We construct new codes matrix multiplication that achieve same fault/straggler previously constructed MatDot Codes Polynomial Codes.2)We show condition number every m ×m sub-matrix an ×n, n ? Chebyshev-Vandermonde matrix, evaluated on n-point Chebyshev grid, grows O(n 2(n-m) ) > m.3)By specializing our orthogonal constructions polynomials, using bound matrices, we numerically stable multiplication. empirically demonstrate have significantly lower errors compared previous approaches involve inversion Vandermonde matrices. generalize explore trade-off between computation/communication fault-tolerance.4)We propose specialization Lagrange approach involves choice evaluation points suitable decoding procedure. is demonstrated standard methods.