Abstract
The total degree algorithm of [3] failed to converge for some delicate approximations because of a wrong Remes one point exchange or an inaccurate eigenvalue (i.e., reference equioscillation error) unless started near an optimal reference. Here we present a modified algorithm that is robust and prove when the revised algorithm’s total degree rational \(\ell _{\infty }\) approximation is optimal for all lesser degrees. Detailed examples and their figures show the bounded eigenvalue computations, steps of the Remes one point exchange for reference searching, and degeneracy pyramids of the revised robust algorithm.
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References
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Kemp, L.F. (2014). On Nondegenerate Rational Approximation. In: Fasshauer, G., Schumaker, L. (eds) Approximation Theory XIV: San Antonio 2013. Springer Proceedings in Mathematics & Statistics, vol 83. Springer, Cham. https://doi.org/10.1007/978-3-319-06404-8_15
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DOI: https://doi.org/10.1007/978-3-319-06404-8_15
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