Research Article

A Method to Accelerate the Convergence of the Secant Algorithm

Table 2

Example of the convergence properties of the second-order accelerated Secant algorithm. The three subsequences () are shown in the columns 2, 3 and 4. The convergence properties for the subsequence are shown in the last column. The ratio is expected to converge to ; compare or confer Theorem 6.


−1
00.1
1
2
3
44.1423
51.2784
61.3159
71.5280
82.3928
91.3822
101.4945
111.6974
121.8855
131.4857
141.5969
151.7063
161.7153
171.5606
181.6392
191.6827
201.6594
211.6052
221.6511
231.6631