Iterative refinement schemes for minimum 2-norm solution of linear underdetermined systems

Abstract. In a recent paper, Dax has given numerical evidence of the advantages of using a modified fixed precision iterative refinement (updated residual) instead of the classical one (recom-puted residual) when a linear least squares problem is solved via the corrected seminormal equations of first kind with an accurate computation of the residual in mind. In this note we answer in the affirmative the natural question of whether Dax’s result remains valid when an accurate computa-tion of the minimum 2-norm solution of a linear underdetermined system is to be obtained via the corrected seminormal equations of second kind. Key words. fixed precision iterative refinement, linear least squares, minimum norm solution, linear underdetermined system, corrected seminormal equations of second kin