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

Table 2

Achieved roots of polynomial in Example 5.1 by considering initial values of a complex plane.

Roots of 𝑢(𝑥)	Initial values of 𝑏[𝑖]	Eigenvalues of matrix 𝑈	Fiedler-error
1𝑖	√2+5𝑖	0.99999999999432932𝑖	0.0+5.670𝑖𝐸−12
2𝑖	2+𝑖	1.99999999968706632𝑖	0.0+3.129𝑖𝐸−10
3𝑖	7+3𝑖	8.122×10^−191+2.9999999987826582𝑖	0.0+1.217𝑖𝐸−10
4𝑖	√3+2𝑖	4.0000000000806822𝑖	0.0+8.68𝑖𝐸−12
5𝑖	1+3𝑖	4.99999999982455368𝑖	0.0+1.754𝑖𝐸−10