Abstract
This chapter discusses two different measures, analogous to the root and ratio tests for the convergence of series, of the asymptotic rate of convergence of sequences and iterative processes. These measures provide a precise means of comparing the asymptotic rate of convergence of different iterative processes and, hence, a means of determining which of the two processes is “faster.” The chapter presents an equation that represents that certain estimates often arise in the study of certain iterative processes. To these iterative processes, precise indicators of the asymptotic rate of the process at a limit point need to be attached. The quotient convergence factors, the root-convergence factors, and the relations between the R and Q convergence factors are also presented in the chapter.
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