Research Article

A Method to Accelerate the Convergence of the Secant Algorithm

Table 1

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


00.1
1
2
33.5652
41.1617
51.3240
62.1850
71.3365
81.5376
91.7857
101.4594
111.5937
121.6519
131.5280
141.5998
151.6060
161.5613
171.5954
181.5910
191.5761
201.5910
211.5865
221.5821
231.5882
241.5855
251.5845
261.5868