Empirical Study of AK' iteration algorithm for initial value ${\mathfrak{a}}^{\left(1\right)}=40$ .

Iterative Sequence

AK' (8)

K* (7)

S (5)

${\mathfrak{a}}^{\left(1\right)}$

40

40

40

${\mathfrak{a}}^{\left(2\right)}$

14.9097

20.0045

30.4216

${\mathfrak{a}}^{\left(3\right)}$

1.30275

10.2608

23.1957

${\mathfrak{a}}^{\left(4\right)}$

1.00014

3.19905

13.632

${\mathfrak{a}}^{\left(5\right)}$

1.

2.07159

10.5296

${\mathfrak{a}}^{\left(6\right)}$

1.

1.52218

8.1891

${\mathfrak{a}}^{\left(7\right)}$

1.

1.25446

6.42346

${\mathfrak{a}}^{\left(8\right)}$

1.

1.124

5.09146

${\mathfrak{a}}^{\left(9\right)}$

1.

1.

3.