Improved Qrginv Algorithm for Computing Moore-Penrose Inverse Matrices

Table 11

Error and computational time results for magic (rank = 3, cond = 5.3481𝑒+019).

Method	Method	Time	‖𝐴𝐴^†𝐴−𝐴‖2	‖𝐴^†𝐴𝐴^†−𝐴^†‖2	‖(𝐴𝐴^†)^𝑇−(𝐴𝐴^†)‖2	‖(𝐴^†𝐴)^𝑇−(𝐴^†𝐴)‖2
WELL1033_Z	qrginv	0.6277	2.1186𝑒−013	3.6375𝑒−011	1.4406𝑒−011	1.8819𝑒−013
	IMqrginv	0.3300	3.1283𝑒−014	2.5635𝑒−011	2.4875𝑒−012	9.1501𝑒−014
WELL1850_Z	qrginv	3.8271	1.0218𝑒−012	5.2163𝑒−011	5.6680𝑒−011	3.5487𝑒−013
	IMqrginv	1.7559	4.0066𝑒−014	6.3726𝑒−012	1.9053𝑒−012	7.7633𝑒−014
ILCC1033_Z	qrginv	0.6119	1.4956𝑒−010	1.1845𝑒−005	1.1674𝑒−006	6.9918𝑒−011
	IMqrginv	0.3786	2.3305𝑒−011	8.1774𝑒−006	1.5766𝑒−008	5.6012𝑒−010
ILCC1850_Z	qrginv	3.9197	1.9075𝑒−011	1.9254𝑒−008	9.4935𝑒−009	1.1185𝑒−011
	IMqrginv	1.6791	2.2511𝑒−013	9.5637𝑒−009	1.2945𝑒−010	6.6275𝑒−012
WATT1_Z	qrginv	10.5110	7.1357𝑒−007	1.8762𝑒−005	6.1068	7.4875𝑒−009
	IMqrginv	3.1018	7.1357𝑒−007	6.4114𝑒−006	6.1068	7.4875𝑒−009
GR-30-30_Z	qrginv	3.1095	2.3077𝑒−011	5.3574𝑒−011	3.5492𝑒−010	3.7356𝑒−013
	IMqrginv	1.6834	3.2708𝑒−013	1.2685𝑒−011	4.9654𝑒−012	2.3249𝑒−013
ADD20_Z	qrginv	60.9176	2.1032𝑒−008	4.9866𝑒−004	2.7022𝑒−004	1.4014𝑒−008
	IMqrginv	59.0933	9.3835𝑒−011	2.0676𝑒−005	8.6123𝑒−007	1.0353𝑒−009
NOS3_Z	qrginv	4.3836	1.6638𝑒−009	2.6309𝑒−009	5.4663𝑒−008	2.1929𝑒−011
	IMqrginv	3.0214	8.6964𝑒−011	8.4269𝑒−011	9.9464𝑒−010	2.1778𝑒−011
SHERMAN1_Z	qrginv	4.3150	1.0363𝑒−009	4.5703𝑒−007	7.4492𝑒−007	3.0278𝑒−010
	IMqrginv	1.3069	1.6398𝑒−012	3.2617𝑒−007	1.4722𝑒−009	5.6796𝑒−012