Eritque Arcus Math Notes

convergence rate

1 min read

sequence converges rate

if

limπ‘˜β†’βˆžβ€–π‘’π‘˜+1β€–β€–π‘’π‘˜β€–π‘Ÿ=𝐢

where 𝐢 is finite nonzero constant, we can say it convergent with rate π‘Ÿ
and

  • π‘Ÿ=1: linear (C < 1)
  • π‘Ÿ>1: super linear
  • π‘Ÿ=2: quadratic

also

  • |𝑔′(π‘₯βˆ—)|<1 it can converge given acceptable interval
  • |𝑔′(π‘₯βˆ—)|>1 it will diverge
  • |𝑔′(π‘₯βˆ—)|=0 it’s at least quadratic

Graph View

Backlinks