Table 3.

Real-world problems and corresponding running times in seconds. DGELSD does not take advantage of sparsity, with its running time determined by the problem size. Though SPQR may not output min-length solutions to rank-deficient problems, we still report its running times (marked with “ * ”). Blendenpik either does not apply to rank-deficient problems or runs out of memory (OOM). LSRN’s running time is mainly determined by the problem size and the sparsity.

Matrix	m	n	nnz	Rank	Cond	DGELSD	SPQR	Blendenpik	LSRN
landmark	71952	2704	1.15e6	2671	1.0e8	18.64	4.920*	-	17.89
rail4284	4284	1.1e6	1.1e7	full	400.0	> 3600	505.9	OOM	146.1
tnimg_1	951	1e6	2.1e7	925	-	510.3	72.14*	-	41.08
tnimg_2	1000	2e6	4.2e7	981	-	1022	168.6*	-	82.63
tnimg_3	1018	3e6	6.3e7	1016	-	1628	271.0*	-	124.5
tnimg_4	1019	4e6	8.4e7	1018	-	2311	371.3*	-	163.9
tnimg_5	1023	5e6	1.1e8	full	-	3105	493.2	OOM	197.6