A Highly Efficient Computer Method for Solving Polynomial Equations Appearing in Engineering Problems

Table 15

Simultaneous finding of all distinct roots of linear combination of Legendre polynomial.

Method

n

CPU

e1

e5

PJM10

3

1.143

1.0e − 3

1.1e − 2

7.5e − 6

0.1e − 3

1.2e − 5

3.5e − 4

4.1e − 3

2.1e − 3

6.1e − 5

1.1e − 3

GFLM15D

3

1.748

2.1e − 110

1.3e − 125

6.7e − 100

2.0e − 27

3.2e − 25

3.6e − 88

1.2e − 15

1.7e − 75

3.5e − 65

1.7e − 105

MMN14D

3

1.015

1.1e − 125

3.8e − 125

4.8e − 126

3.7e − 126

1.8e − 126

1.0e − 127

1.0e − 127

1.0e − 127

2.1e − 126

9.7e − 126