A Modification to the Discrete $l_1 $ Linear Approximation Algorithm of Barrodale and Roberts
Stephen C. Banks, Howard L. Taylor · SIAM Journal on Scientific and Statistical Computing · 1980
A modification to the discrete $l_1 $ linear approximation algorithm of Barrodale and Roberts allows the determination of the vector x that minimizes $\|e\|_1 + \|x\|_1 $, where e is the residual vector defined by the linear system $Ax + e = b$. The matrix A is $m \times n$, where m is not necessarily greater than or equal to n. Computational and storage properties of the unmodified algorithm are preserved.