Desirable characteristics include a rapid rate of convergence, ability to separate close roots, robustness against failures of differentiability, and low propagation rate of rounding errors.
32.
An example of a nonlinear sequence transformation is Aitken's delta-squared process, used to improve the rate of convergence of a slowly convergent sequence.
33.
This transformation is commonly used to improve the rate of convergence of a slowly converging sequence; heuristically, it eliminates the largest part of the absolute error.
34.
:: : : : : The limit as such is just 1, the more complicated expression provides info on the rate of convergence towards the limit.
35.
The rate of convergence depends on the separation between eigenvalues, so a practical algorithm will use shifts, either explicit or implicit, to increase separation and accelerate convergence.
36.
If they are not, a run of " bad luck " could lead to the wider interval being used many times, thus slowing down the rate of convergence.
37.
These two tectonic plates currently converge at a rate of } } to } } per year, only about half the rate of convergence from seven million years ago.
38.
However, the rate of convergence highly depends on the first guessing condition, and there is no way to find a proper one, except through trial and error.
39.
His main achievements concern approximation theory in particular the theory of Pad?approximants and its application in numerical methods for improving the rate of convergence of sequences of real numbers.
40.
These cases can occur because the definition of the G�teaux derivative only requires that the difference quotients converge along each direction individually, without making requirements about the rates of convergence for different directions.
