Correction to: Polynomials with bounds and numerical approximation

Abstract

The result of the main Theorem 2.8 in Després (2017) remains unchanged. Nevertheless the proof must be corrected due to one missprint and missing low order contributions. This correction has its importance in case one desires to implement the method, which is part of our current research.We use the notations of [1]. The missprint shows up in formula (24), where D was replaced by C in the expressions of b and c. Formula (24) now becomesThe main correction comes from missing terms proportional to B n−2 and D n−2 in formula (25). Formula (25) now becomesThe online version of the original article can be found at https://doi

A projection algorithm on the set of polynomials with two bounds

“…The structure of the proof [3,4] is as follows. One starts from q P U n and shows that there exists e 1 P U 1 such that e 1 q P U n´1 .…”

“…To do so we will use the iterative decomposition technique developped in the theoretical proof of [3,4] with an additional correction step.…”

“…In the next section we introduce some elementary concepts and notation, and we specify some of the aforementioned algebraic properties: the quaternion structure is recalled, its expression in the Chebychev basis is given and some norms are defined. In Section 3 we then specify our approximation problem with two bounds and define the nonlinear projection algorithm: it is an extension of the theoretical decomposition method from [3,4] with a new nonlinear correction step. In Section 4 we perform the numerical analysis of the method and state in Theorem 4.2 a continuity or stability result.…”