Improved Qrginv Algorithm for Computing Moore-Penrose Inverse Matrices

Table 1

Error and computational time results for random singular matrices.

𝑛	Method	Time	‖𝐴𝐴^†𝐴−𝐴‖2	‖𝐴^†𝐴𝐴^†−𝐴^†‖2	‖(𝐴𝐴^†)^𝑇−(𝐴𝐴^†)‖2	‖(𝐴^†𝐴)^𝑇−(𝐴^†𝐴)‖2
2^7	qrginv	0.0317	3.4169𝑒−014	0.2638𝑒−016	5.7671𝑒−015	3.2645𝑒−015
	IMqrginv	0.0137	1.6175𝑒−014	3.7297𝑒−016	3.0344𝑒−015	2.5228𝑒−015
2^8	qrginv	0.1176	1.0052𝑒−013	9.9243𝑒−016	8.0286𝑒−015	4.0476𝑒−015
	IMqrginv	0.0786	2.9804𝑒−014	3.4041𝑒−016	3.8500𝑒−015	3.1148𝑒−015
2^9	qrginv	1.0584	1.3649𝑒−013	1.0186𝑒−015	1.1006𝑒−014	4.9494𝑒−015
	IMqrginv	0.8236	5.3456𝑒−014	5.0122𝑒−015	5.0122𝑒−015	3.8394𝑒−015
2^10	qrginv	10.8336	2.6266𝑒−013	1.0616𝑒−015	1.4943𝑒−014	5.9069𝑒−015
	IMqrginv	8.2976	8.8502𝑒−014	2.9117𝑒−016	6.3837𝑒−015	4.8854𝑒−015
2^11	qrginv	81.1429	4.9931𝑒−013	1.1850𝑒−015	2.1858𝑒−014	7.2568𝑒−015
	IMqrginv	55.0746	1.6676𝑒−013	2.5936𝑒−016	8.3743𝑒−015	6.5585𝑒−015