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Interpolation of continuous maps by piecewise-linear maps. (English) Zbl 0408.41002


MSC:

41A05 Interpolation in approximation theory
41A30 Approximation by other special function classes

Citations:

Zbl 0391.41001
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References:

[1] C. Rourke and B. Sanderson, Introduction to Piecewise Linear Topology, Springer-Verlag, New York. · Zbl 0254.57010
[2] V. N. Malozemov, ”On the deviation of broken lines,” Vestn. Leningr. Gos. Univ.,7, 150–153 (1966).
[3] V. F. Babenko and A. A. Ligun, ”On interpolation by polyhedral functions,” Mat. Zametki,18, No. 6, 803–814 (1975). · Zbl 0318.41024
[4] B. Delaunay, ”Sur la sphère vide,” Izv. Akad. Nauk SSSR, Ser. Mat.,6, 793–800 (1934). · Zbl 0010.41101
[5] B. N. Delaunay and S. S. Ryshkov, ”Extremal problems in the theory of positive quadratic forms,” Tr. Mat. Inst., Akad. Nauk SSSR,112, 203–223 (1971).
[6] A. F. Gametskii, ”On the optimality of the principal lattice of the first Voronoi type among lattices of the first type for any number of measurements,” Dokl. Akad. Nauk SSSR,151, No. 3, 482–484 (1963).
[7] R. Kershner, ”The number of circles covering a set,” Am. J. Math.,61, 665–671 (1939). · JFM 65.0197.03 · doi:10.2307/2371320
[8] R. P. Bambah, ”On lattice covering by spheres,” Proc. Nat. Acad. Sci. India,20, 25–52 (1954). · Zbl 0059.16301
[9] B. N. Delaunay and W. S. Ryshkov, ”Solution of the problem of the least dense lattice covering of four-dimensional space by congruent balls,” Dokl. Akad. Nauk SSSR,152, No. 3, 523–524 (1963).
[10] S. S. Ryshkov and E. P. Baranovskii, ”Solution of the problem of the least dense lattice covering of five-dimensional space by congruent balls,” Dokl. Akad. Nauk SSSR,222, No. 1, 39–42 (1971).
[11] S. S. Ryshkov, ”Some remarks on the types of n-dimensional parallelohedra and the density of lattice coverings of a space by congruent balls,” Dokl. Akad. Nauk SSSR,162, No. 2, 277–280 (1965).
[12] G. F. Voronoi, ”Studies on primitive parallelohedra,” in: Collected Works [in Russian], Vol. 2 Izd. Akad. Nauk SSSR, Moscow (1952), pp. 239–368.
[13] S. S. Ryshkov, ”Effectivization of a method of Davenport in the theory of coverings,” Dokl. Akad. Nauk SSSR,175, No. 2, 303–306 (1967). · Zbl 0157.52604
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