Simple rational approximation: Difference between revisions

Revision as of 06:55, 28 January 2010

Revision as of 11:11, 25 February 2010

Line 27:

:<math>g(x)=1-\frac{\alpha}{{f(x)}}=0.</math>

This one-point second-order method is known to show a locally quadratic convergence if the root of equation is simple.

SRA strictly implies this one-opintpoint second-order interpolation by a simple rational function.

We can notice that even third order method is a variation of Newton's method. We see the Newton's steps are multiplied by some factors. These factors are called the ''convergence factors'' of the variations, which are useful for analyzing the rate of convergence. See Gander(1978).

This article is not fully able to explain what does <math>\alpha</math> mean or any method by which it could be determined.

== References ==