Geodesic
On the polynomials, the least deviating from zero in $L[-1,1]$ metrics
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 3, pp. 223-238.

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For polynomials, the least deviating from zero in $L[-1,1]$ metrics with given number of leading coefficients, it is obtained the representation through the so-called extremal polynomials of the least deviation, whose number of sign changes is equal to their degree. The instruments of effective calculating of these polynomials are represented. 
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V. È. Gheit. On the polynomials, the least deviating from zero in $L[-1,1]$ metrics. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 3, pp. 223-238. http://geodesic.mathdoc.fr/item/SJVM_1999_2_3_a2/

[1] Korkin A. N., Zolotarev G. I., “Sur une certain minimum”, Nouv. Ann. de math. Ser. 2, 1873, no. 12, 337–355

[2] Galeev E. M., “Zadacha Zolotareva v metrike $L[-1,1]$”, Mat. zametki, 7:1 (1975), 13–19 | MR

[3] Timan A. F., Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960

[4] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, Izd-vo MGU, M., 1976 | MR

[5] Geit V. E., O forme zolotarevskikh polinomov v prostranstve $L[-1,1]$, 22.04.98, No 1228-V98, VINITI, M., 1998

[6] Geit V. E., Reshenie $L$-problemy Zolotareva v odnom chastnom sluchae, 27.11.98, No 3492-V98, VINITI, M., 1998

[7] Geit V. E., Tez. dokl. Vseros. nauch. konf. “Algoritmicheskii analiz nekorrektnykh zadach”, Izd-vo UrGU, Ekaterinburg, 1998