Convergence of Hölder projections to chebyshev projections
V. I. Zorkal'tsev
Limnological Institute, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033 Russia
The problem of finding a point of a linear manifold with a minimal weighted Chebyshev norm is considered. In particular, to such a problem, the Chebyshev approximation is reduced. An algorithm that always produces a unique solution to this problem is presented. The algorithm consists in finding relatively internal points of optimal solutions of a finite sequence of linear programming problems. It is proved that the solution generated by this algorithm is the limit to which the Hölder projections of the origin of coordinates onto a linear manifold converge with infinitely increasing power index of the Hölder norms using the same weight coefficients as the Chebyshev norm.
Hölder norms, Chebyshev norms, Hölder projections, Chebyshev projections, Chebyshev approximation, Haar condition, relatively interior points of optimal solutions.
Computational Mathematics and Mathematical Physics, 2020, 60:11, 1810–1822
V. I. Zorkal'tsev, “Convergence of Hölder projections to chebyshev projections”, Zh. Vychisl. Mat. Mat. Fiz., 60:11 (2020), 1867–1880; Comput. Math. Math. Phys., 60:11 (2020), 1810–1822
Citation in format AMSBIB
\paper Convergence of H\"older projections to chebyshev projections
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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