To approximate a simple root of a real function f we construct a family of iterative maps, which we call Newton-barycentric functions, and analyse their convergence order. The performance of the resulting methods is illustrated by means of numerical examples.
Keywords:
order of convergence; Newton's method; Newton-barycentric map; nonlinear equations
| Iterative function | Error | Number of iterations | Number of function evaluations |
|---|---|---|---|
| t0 | 2.13 × 10-11 | 3 | 6 |
| t1 | -4.54 × 10-17 | 2 | 6 |
| t2 | -4.54 × 10-11 | 1 | 5 |
| Iterative function | Error | Number of iterations | Number of function evaluations |
|---|---|---|---|
| t0 | 1.03 × 10-11 | 3 | 6 |
| t1 | 3.8 × 10-23 | 2 | 6 |
| t2 | -3.3 × 10-16 | 1 | 5 |
| Iterative function | Error | Number of iterations | Number of function evaluations |
|---|---|---|---|
| t0 | 2.3 × 10-13 | 4 | 8 |
| t1 | 1.8 × 10-13 | 3 | 9 |
| t2 | 4.8 × 10-19 | 2 | 10 |
