2021/08/02 by М. В. Невский, Nevskii, Mikhail, Alexey Ukhalov +1
Computer Science · Engineering · Mathematics · #41A05 #52B55 #52C07 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2108.00880
openalex publication_date 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper contains a survey of results obtained by the authors mostly during the past few years and published by 2021. In particular, we present the best of known estimates of numerical characteristics related to the research theme. Sections: 1. Introduction. 2. The case when n+1 is an Hadamard number. 3. Estimates for the minimal absorption index of a cube by a simplex. 4. Estimates for the minimal norm of a projector in linear interpolation on a cube in \mathbb Rn. 5. Estimates of numbers ξn^′ and θn^′. 6. Simplices satisfying the inclusions S⊂ Qn⊂ nS. 7. Perfect simplices. 8. Equisecting simplices. 9. Properties of (0,1)-matrices of order n having maximal determinant. 10. Problems for a simplex and a Euclidean ball. 11. Linear interpolation on a Euclidean ball. Bibliography: 56 titles. Keywords: simplex, cube, Euclidean ball, homothety, axial diameter, absorption index, Hadamard number, interpolation, projector, norm, estimate.