We {formalize the} definition of a stable algorithm that is (i) adapted to the use of multiple and variable precision arithmetic, (ii) sufficiently close to the actual practice of computing to be useful, and (iii) sufficiently robust from a mathematical point of view as to allow for the rigorous proof of theorems. This allows us to state some widely satisfied hypotheses, depending only on two functions $f$ and $g$, under which the composition of a stable algorithm for $f$ and a stable algorithm for $g$ is a stable algorithm for the composition $f \circ g$.

翻译：我们{正式化}对稳定算法的定义是:(一) 适应多种和可变精确算术的使用,(二) 足够接近计算的实际做法,因而有用,和(三) 从数学角度来说,足够稳健,可以对理论进行严格证明,这使我们能够说明一些普遍满意的假设,仅取决于两个函数f美元和g美元,根据这两个函数,美元和g美元的稳定算法的组成是构成美元/circg美元的稳定的算法。