Algorithms of constrained uniform approximation
<|reference_start|>Algorithms of constrained uniform approximation: We address the problem of the best uniform approximation of a continuous function on a convex domain. The approximation is by linear combinations of a finite system of functions (not necessarily Chebyshev) under arbitrary linear constraints. By modifying the concept of alternance and of the Remez iterative procedure we present a method, which demonstrates its efficiency in numerical problems. The linear rate of convergence is proved under some favourable assumptions. A special attention is paid to systems of complex exponents, Gaussian functions, lacunar algebraic and trigonometric polynomials. Applications to signal processing, linear ODE, switching dynamical systems, and to Markov-Bernstein type inequalities are considered.<|reference_end|>
@article{protasov2024algorithms,
    title={Algorithms of constrained uniform approximation},
    author={Vladimir Yu. Protasov, Rinat Kamalov},
    journal={arXiv preprint arXiv:2403.16330},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.16330},
    primaryClass={math.NA cs.NA math.FA math.OC}
}