It seems R-convergence and Q-convergence, when refering to order of convergence, is used interchangeably in the literature sometimes. (For example, I've been looking at the proof of the convergence rate of the secant method.) In "Iterative Solution of Nonlinear Equations in Several Variables" by J. M. Ortega and W. C. Rheinboldt (1987), Chapter 9, I read up on the definitions but I do not quite understand them. So, I have questions about them:
- What is the difference between these definitons and where did they come from (i.e. why are there different definitions)?
- Are these definitions equivalent? If so, how do you get from one to the other?