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This paper deals with the polynomial linear system solving with errors(PLSwE) problem. Specifically, we focus on the evaluation-interpolationtechnique for solving polynomial linear systems and we assume that errors canoccur in the evaluation step. In this framework, the number of evaluationsneeded to recover the solution of the linear system is crucial since it affectsthe 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 thisnumber of evaluations. We proved in [Guerrini et al., Proc. ISIT'19] that iferrors are randomly distributed, the bound of the number of evaluations can belowered 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 thedependency on the parameters of the linear system, based on work of [Cabay,Proc. SYMSAC'71]. Second, we introduce an early termination strategy in orderto handle the unnecessary increase of the number of evaluations due tooverestimation of the parameters of the system and on the bound on the numberof errors.

Polynomial Linear System Solving with Random Errors: new bounds and early termination technique