Choosing Improved Initial Values for Polynomial Zerofinding in Extended Newbery Method to Obtain Convergence

Table 3

Achieved roots of polynomial by choosing initial values on the circle.

Roots of 𝑢(𝑥)	Initial values of 𝑏[𝑖]	Eigenvalues of matrix 𝑈	Fiedler error
11	1+3𝑖	11.000000036818370	3.681𝐸−8
12	−1−3𝑖	11.9999999996290109	3.709𝐸−8
13	√2+√8𝑖	13.0000000034938808	3.493𝐸−8
14	−√2−√8𝑖	13.9999999957633268	4.236𝐸−8