Table 2.

Comparing LSRN’s solution accuracy to DGELSD. DGELSD’s solution is denoted by x*, and LSRN’s denoted by x̂. The metrics are computed using quad precision. We show the average values of those metrics from 50 independent runs. LSRN should be accurate enough for most applications.

	$\frac{{\Vert \mathrm{x̂}\Vert }_2-{\Vert x^{*}\Vert }_2}{c{\Vert x^{*}\Vert }_2}$	$\frac{{\Vert A\mathrm{x̂}-b\Vert }_2{\Vert A{x}^{*}-b\Vert }_2}{c{\Vert A{x}^{*}-b\Vert }_2}$	$\frac{{\Vert A^T(A{x}^{*}-b)\Vert }_2}{c}$	$\frac{{\Vert A^T(A\mathrm{x̂}-b)\Vert }_2}{c}$
Full rank	−8.5e-14	0.0	3.6e-18	2.5e-17
Rank-def	−5.3e-14	0.0	8.1e-18	1.5e-17
Approx. rank-def	9.9e-12	−7.3e-16	2.5e-17	2.7e-17