An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems

Table 1

Comparing the numerical results for Example  2 with different methods.

Solutions	𝑥1	𝑥2	𝑥3	𝑥4	𝑥5	𝑥6	𝑥7	𝑥8	𝑥9
Exact	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
SVD	0.9999	1.008	0.985	0.995	1.007	1.012	1.009	0.999	0.984
SDM	1.00001	0.99980	1.00091	0.99910	0.99928	1.00035	1.00103	1.00062	0.99898
CGM	1.00000	1.00001	0.99924	1.00019	0.99988	0.99985	1.00008	1.00019	0.99987
RSDM	1.00000	0.99986	1.00087	0.99888	0.99928	1.00058	1.00128	1.00066	0.99856
OGSDA	0.9999999999	1.000000005	0.9999999185	1.000000569	0.9999979488	1.000004126	0.9999953195	1.000002797	0.9999993151