On the uniqueness of simultaneous rational function reconstruction

Guerrini, Eleonora; Lebreton, Romain; Zappatore, Ilaria

doi:10.1145/3373207.3404051

Cited by 2 publications

(1 citation statement)

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“…vector Cauchy interpolation) to recover the solution ( ). Note that if one wants to take advantage of the common denominator of ( ), then vector Cauchy interpolation should be replaced by simultaneous rational function reconstruction [8,15,16]; in this paper we do not consider this case.…”

Section: Introductionmentioning

confidence: 99%

Polynomial Linear System Solving with Random Errors

Guerrini

Lebreton

Zappatore

2021

Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation

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This paper deals with the polynomial linear system solving with errors (PLSwE) problem. More specifically, we solve linear systems with univariate polynomial coefficients via an evaluationinterpolation technique assuming that errors can occur before the interpolation step. In this framework, the number of evaluations needed to recover the solution depends on the parameters of the linear system (degrees, size) and on the number of errors.Our work is part of a series of papers about PLSwE aiming to reduce this number of evaluations, which is crucial since it affects the complexity. We proved in [7] that if errors are randomly distributed, the bound on the number of evaluations can be lowered with respect to the error rate.In this paper, following the approach of [9], we improve the results of [7] in two directions. First, we propose a new bound on the number of evaluations, lowering the dependency on the parameters of the linear system, based on the work of [5]. Second, we introduce an early termination strategy in order to handle the unnecessary increase of the number of evaluations due to the overestimation of the output degrees and of the number of errors. CCS CONCEPTS• Mathematics of computing → Coding theory; • Computing methodologies → Algebraic algorithms; Linear algebra algorithms.

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Section: Introductionmentioning

confidence: 99%