The Continuous Newton's Method, Inverse Functions, and Nash-Moser

@article{Neuberger2007TheCN,
  title={The Continuous Newton's Method, Inverse Functions, and Nash-Moser},
  author={J. W. Neuberger},
  journal={The American Mathematical Monthly},
  year={2007},
  volume={114},
  pages={432-437}
}
The conventional Newton’s method for finding a zero of a function F : R → R, assuming that (F ′(y))−1 exists for at least some y in R, is the familiar iteration: pick z0 in R n and define zk+1 = zk − (F ′(zk))−1F (zk) (k = 0, 1, 2, . . . ), hoping that z1, z2, . . . converges to a zero of F . What can stop this process from finding a zero of F ? For one… CONTINUE READING