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Found 2 papers, 1 papers with code
Fast, Provably convergent IRLS Algorithm for p-norm Linear Regression
However, these algorithms often diverge for p > 3, and since the work of Osborne (1985), it has been an open problem whether there is an IRLS algorithm that is guaranteed to converge rapidly for p > 3.
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 $p \in (1, 2) \cup (2,\infty).$ Our 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 $m \times m$ linear system, $m$ being the dimension of the ambient space.
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