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

Table 4

Achieved roots of polynomial in Example 7.1 by considering initial values (one of the approximations is away from real value).

Roots of 𝑢(𝑥)	Initial values of 𝑏[𝑖]	Eigenvalues of matrix 𝑈	Fiedler error
1	3.9	0.99999999999961600	5.293𝐸−11
2	13.3	1.99999999999998450	1.023𝐸−7
3	2.1	2.99999999999999287	2.476𝐸−11
4	1.5	3.9999999999999702	1.524𝐸−11