Ein Einschliessungsverfahren für Lösungen Fehlerbehafteter Linearer Gleichungen

Abstract

In a partially ordered space, the method x_n+1 = L⁺x ⁺_n − N⁺x ^-_n − L⁻y⁺ + N⁻ y ^-_n + r, y_n+1 = N⁺y⁺ − L⁺y ^-_n − N⁻x ⁺_n + L⁻x⁻ + t of successive approximation is developed in order to enclose the solutions of a set of linear fixed point equations monotonously. The method works if only the inequalities x₀ ≤ y₀, x₀ ≤ x₁, y₁ ≤ y₀ related to the starting elements are satisfied. In finite-dimensional spaces suitable starting vectors can be computed if a sufficiently good approximation for the fixed points is known.