A sequence x0,x1, superconverges to 0 if, when the xi are written in base 2, then each number xi starts with 2i-12i zeroes. For example, the following sequence is superconverging to 0.


In this case it is easy to see that the number of binary 0’s doubles each xn.

A sequence {xi} superconverges to x if {xi-x} superconverges to 0, and a sequence {yi} is said to be superconvergent if there exists a y to which the sequence superconverges.

Title superconvergence
Canonical name Superconvergence
Date of creation 2013-03-22 11:58:12
Last modified on 2013-03-22 11:58:12
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 15
Author mathcam (2727)
Entry type Definition
Classification msc 41A25
Synonym superconverge
Related topic NewtonsMethod
Related topic KantorovitchsTheorem
Related topic SuperincreasingSequence