Iterative Refinement for $ell_p$-norm Regression

We give improved algorithms for the $ell_{p}$-regression problem, $min_{x} |x|_{p}$ such that $A x=b,$ for all $p (1,2) cup (2,infty).$ algorithms obtain a high accuracy solution in $tilde{O}_{p}(m^{frac{|p-2|}{2p + |p-2|}}) le tilde{O}_{p}(m^{frac{1}{3}})$ iterations, where each iteration requires solving an $m m$ linear system, $m$ b...More