A modified Seidel method for calculating the fixed points of contractive mappings

For calculating the fixed point of a contractive mapping f = (f1 , f2 , …, fm ) : Ω → Ω, Ω ∈ Rm we employ a modified Seidel successive approxi-

mations scheme: where

(n) (n,k) (n,k) (n,k) (n,k)

xπ(k) = fπ(k)

(n,k)
x l =

x 1 , …, x k−1 , x k , …, x m , (n)

l

We present a strategy to find the permutation π in order to accelerate the iterative processus.

xl , if l = π(s) and s < k, x(n−1), if l = π(s) and s ≥ k.