TY - GEN
T1 - Numerically Stable Polynomially Coded Computing
AU - Fahim, Mohammad
AU - Cadambe, Viveck R.
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - We consider the issue of numerical stability in solving the problem of coded large scale matrix multiplication in distributed systems where worker nodes are prone to failures/delays. We construct new codes that achieve comparable fault tolerance as previous codes, but are more numerically stable. Unlike previous codes that use polynomials expanded in a monomial basis, our codes use polynomials expressed in a basis of orthonormal polynomials. We show via new theoretical results on the condition number, as well as numerical experiments, that the application of these codes can lead to significantly more numerically stable computation than the current monomial-basis codes.
AB - We consider the issue of numerical stability in solving the problem of coded large scale matrix multiplication in distributed systems where worker nodes are prone to failures/delays. We construct new codes that achieve comparable fault tolerance as previous codes, but are more numerically stable. Unlike previous codes that use polynomials expanded in a monomial basis, our codes use polynomials expressed in a basis of orthonormal polynomials. We show via new theoretical results on the condition number, as well as numerical experiments, that the application of these codes can lead to significantly more numerically stable computation than the current monomial-basis codes.
UR - http://www.scopus.com/inward/record.url?scp=85073170158&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2019.8849468
DO - 10.1109/ISIT.2019.8849468
M3 - Conference contribution
AN - SCOPUS:85073170158
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 3017
EP - 3021
BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019
Y2 - 7 July 2019 through 12 July 2019
ER -