Minimax and maximin problems for sums of translates on the real axis

2024/05/14 by Tatiana Nikiforova, Nikiforova, Tatiana · 2 citations
Computer Science · Engineering · #26A51 #26D07 #49K35 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Computational Geometry and Mesh Generation #FOS: Mathematics #Optimization and Packing Problems

paper · pdf · doi:10.48550/arxiv.2405.08561

openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sums of translates generalize logarithms of weighted algebraic polynomials. The paper presents the solution to the minimax and maximin problems on the real axis for sums of translates. We prove that there is a unique function that is extremal in both problems. The key in our proof is a reduction to the problem on a segment. For this, we work out an analogue of the Mhaskar-Rakhmanov-Saff theorem, too.

Cited by

• Homeomorphism theorem for sums of translates on the real axis
• On some examples and counterexamples about weighted Lagrange interpolation with Exponential and Hermite weights

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