Acceleration of iteration methods for interval fixed point problems

We consider the fixed point equation x = F(x) with a continuous and inclusi on isotone interval function F : R-n --> R-n. The iteration x(k+1) = F(x(k) ) converges monotonically (x(k+1) subset of or equal to x(k)) to a fixed po int of F if x(1) subset of or equal to x(0). We prove a theorem on an accel erated monotone iteration and apply it to systems of linear and nonlinear e quations. For linear fixed point equations (x = Ax + b), we also present a modified single step method. (C) 2001 Elsevier Science Inc. All rights rese rved.