On the convergence of the column-updating method (Q1328473)

Some new convergence results are proved for the column-updating method which explains why this method is so good. Briefly speaking, if the linear convergence of the method is assumed, then the convergence is \(R\)- superlinear; if the method is restarted periodically then we obtain local and \(R\)-superlinear convergence; if for \(n=2\) it is superlinearly convergent, then no restarts are necessary for proving local and \(R\)- superlinear convergence.