On Convergents Infinite Products and Some Generalized Inverses of Matrix Sequences

Table 6

Results for a random matrix 𝐴∈ℂ^100×80 using the iteration (2.18).

𝑛	‖𝑋𝐴𝑋−𝑋‖	‖𝐴𝑋𝐴−𝐴‖	‖(𝐴𝑋)^∗−𝐴𝑋‖	‖(𝑋𝐴)^∗−𝑋𝐴‖
1	0.060276	45.097	2.0509	1.5239×10^−4
2	0.089542	45.082	3.9427×10^−1	4.0096×10^−5
3	0.10119	45.081	8.3223×10^−2	8.8403×10^−6
4	0.096287	45.121	1.627×10^−3	1.8814×10^−6
5	0.1096	45.185	3.2587××10^−4	3.8609×10^−7
6	0.12111	45.207	6.1535×10^−5	7.7762×10^−8
7	0.13823	45.146	1.1418×10^−5	1.4853×10^−9
8	0.17182	44.971	2.0472×10^−6	2.9817×10^−10
9	0.21594	44.623	3.5587×10^−7	5.422𝑒×10^−11
10	0.27022	43.962	6.0384×10^−8	9.337×10^−12
11	0.34782	42.688	9.8614×10^−9	1.5714×10^−12
12	0.46134	40.249	1.5947×10^−9	2.5064×10^−13
13	0.62169	35.766	2.5794×10^−10	3.6162×10^−14
14	0.74641	28.232	4.0931×10^−11	4.6385×10^−15
15	0.73592	17.588	6.0751×10^−12	5.0276×10^−16
16	0.39382	6.8259	8.0089×10^−13	3.3054×10^−16
17	0.068122	1.0281	9.0865×10^−14	2.3201×10^−17
18	0.0015796	0.023321	9.2857×10^−15	2.1781×10^−17
19	8.1324𝑒−007	1.2001𝑒−005	9.2907×10^−16	1.7884×10^−17