2022/07/13 by Charalambides, Neophytos, Pilanci, Mert, Hero, Alfred
#12-08 #15A29 #94A15 #94B05 #Cryptography and Security (cs.CR) #E.4 #FOS: Computer and information sciences #FOS: Mathematics #G.1.2 #G.1.6 #Information Theory (cs.IT) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2207.06271
A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion algorithm which does not require a matrix factorization, but uses a black-box least squares optimization solver as a subroutine, to give an estimate of the inverse of a real full-rank matrix. We then present a distributed framework for which our algorithm can be implemented, and show how we can leverage sparsest-balanced MDS generator matrices to devise matrix inversion coded computing schemes. We focus on balanced Reed-Solomon codes, which are optimal in terms of computational load; and communication from the workers to the master server. We also discuss how our algorithms can be used to compute the pseudoinverse of a full-rank matrix, and how the communication is secured from eavesdroppers.