Odds and ends

Two other special issues, to be filed for now.

1. If the root you are after is multiple, convergence may be much slower than expected, especially a Newton or Secant algorithm. The reason is simple to state - at a multiple root, the derivative goes to zero. There are special fixes for multiple roots.{If you are after polynomial roots, there are special techniques that work especially well. When looking for all polynomial roots, deflation is often useful. Decartes' Rule of Signs, and the rational Root Test are helpful also.
2. Fixed point iteration is a method for finding all solutions to the equation x=g(x). The iteration proceeds by setting . One may also use Newton or False Position or other methods on the function f(x)=x-g(x).