This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the evaluation step. In this framework, the number of evaluations needed to recover the solution of the linear system is crucial since it affects the number of computations. It depends on the parameters of the linear system (degrees, size) and on a bound on the number of errors. Our work is part of a series of papers about PLSwE aiming to reduce this number of evaluations. We proved in [Guerrini et al., Proc. ISIT'19] that if errors are randomly distributed, the bound of the number of evaluations can be lowered for large error rate. In this paper, following the approach of [Kaltofen et al., Proc. ISSAC'17], we improve the results of [Guerrini et al., Proc. ISIT'19] in two directions. First, we propose a new bound of the number of evaluations, lowering the dependency on the parameters of the linear system, based on work of [Cabay, Proc. SYMSAC'71]. Second, we introduce an early termination strategy in order to handle the unnecessary increase of the number of evaluations due to overestimation of the parameters of the system and on the bound on the number of errors.

翻译：本文涉及解决错误( PLSwE) 的多线性系统。 具体地说, 我们的工作是一系列关于PLSwE 错误的文件的一部分, 目的是减少评估的数量。 我们在[ Guerrini 等人, Proc. ISIT'19] 中证明, 如果错误是随机分布的, 则评价数量的界限可以降低, 以很大的误差率。 在本文中, 恢复线性系统解决方案所需的评价数量至关重要, 因为它影响到计算数量。 它取决于线性系统的参数( 度、 大小), 并取决于错误数量的约束。 我们的工作是一系列关于PLSwE 错误的文件的一部分, 目的是减少评估的数量。 首先, 我们建议对评估的数量进行新的约束, 降低对SOLMS 的早期端点的依赖性, 引入我们SLISMA 的线性处理系统的早期端点 。