Newton's Method and Fractal Patterns (UMAP)

This module discusses Newton's method as an efficient iterative procedure for approximating zeros of a differentiable function. It claims that Newton's method is intricate even for real polynomials, and in the complex plane it generates beautiful fractal patterns.

Table of Contents:

HOW DOES NEWTON'S METHOD BEHAVE IN THE LARGE?

NEWTON'S METHOD

NEWTON'S METHOD IN THE LARGE: AN EXAMPLE ON THE REAL LINE

NEWTON'S METHOD IN THE COMPLEX PLANE

FURTHER DIRECTIONS

SOLUTIONS TO THE EXERCISES

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR