# Stability of a computational algorithm

A partially resolving operator $L_m^h$, uniformly bounded in $h$ and $m$, describing the succession of steps in the computational algorithm for solving the equation
$$L^hu^h=f^h,$$
for example, a grid equation with step $h$ (cf. Closure of a computational algorithm). Stability of a computational algorithm guarantees weak influence of computational errors on the result of the calculation. However, the possibility is not excluded that the quantity $p(h)=\sup\|L_m^h\|$ grows comparatively slowly and a corresponding strengthening of the influence of computational errors for $h\to0$ remains practically admissible. The concept of stability of a computational algorithm has been made concrete in applications to grid-projection methods (cf. [4]) and in applications to iterative methods (cf. [6]). There are also other definitions of the stability of a computational algorithm (cf. e.g. [1], [3]).