In this paper, we present novel deterministic algorithms for multiplying two n \times n matrices approximately. Given two matrices A,B we return a matrix C' which is an \emph{approximation} to C = AB. We consider the notion of approximate matrix multiplication in which the objective is to make the Frobenius norm of the error matrix C-C' arbitrarily small. Our main contribution is to first reduce the matrix multiplication problem to solving a set of linear equations and then use standard techniques to find an approximate solution to that system in \tilde{O}(n^2) time. To the best of our knowledge this the first examination into designing quadratic time deterministic algorithms for approximate matrix multiplication which guarantee arbitrarily low \emph{absolute error} w.r.t. Frobenius norm.
ECCC TR14-117 presents an efficient iterative algorithm that purportedly computes an approximation to the product of two n \times n matrices. On this comment we show that, in fact, the algorithm converges to a diff erent matrix than the product matrix.
