Geodesic
Optimal extrapolation of polynomials given with error
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 265-275 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The problem of optimal extrapolation of polynomials given with an error on a compact set is studied. Its relationship with Chebyshev's problem on a polynomial that least deviates from zero on a compact set is established. An exact solution to the problem of optimal extrapolation of polynomials is obtained for the case when the compact set is a lemniscate. An exact solution is written for the problem of extrapolation from the interval $[-1,1]$ to the real line.
Keywords: optimal extrapolation of polynomials, optimal recovery of functionals, Chebyshev polynomial of a compact set. 
@article{TIMM_2024_30_4_a20,
     author = {A. A. Trembach},
     title = {Optimal extrapolation of polynomials given with error},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {265--275},
     year = {2024},
     volume = {30},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a20/}
}
TY  - JOUR
AU  - A. A. Trembach
TI  - Optimal extrapolation of polynomials given with error
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2024
SP  - 265
EP  - 275
VL  - 30
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a20/
LA  - ru
ID  - TIMM_2024_30_4_a20
ER  - 
%0 Journal Article
%A A. A. Trembach
%T Optimal extrapolation of polynomials given with error
%J Trudy Instituta matematiki i mehaniki
%D 2024
%P 265-275
%V 30
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a20/
%G ru
%F TIMM_2024_30_4_a20
A. A. Trembach. Optimal extrapolation of polynomials given with error. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 265-275. http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a20/

[1] Osipenko K.Yu., Vvedenie v teoriyu optimalnogo vosstanovleniya, Lan, SPb., 2022, 388 pp.

[2] Arestov V.V., “Priblizhenie neogranichennykh operatorov ogranichennymi i rodstvennye ekstremalnye zadachi”, Uspekhi mat. nauk, 51:6 (312) (1996), 89–124 | DOI | MR | Zbl

[3] Walsh J.L., Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc., Rhode Island, 1960, 405 pp. | MR | Zbl

[4] Chebyshev P.L., “Teoriya mekhanizmov, izvestnykh pod nazvaniem parallelogrammov”, Polnoe sobranie sochinenii P. L. Chebysheva, v 5 t., v. 2, Matematicheskii analiz, AN SSSR, M.; L., 1947, 23–51 | MR

[5] Faber G., “Über Tschebyscheffsche Polynome”, J. reine und angew. Math., 150 (1920), 79–106 | DOI | MR

[6] Milovanović G.V., Mitrinović D.S., Rassias Th.M., Topics in polynomials: Extremal problems, inequalities, zeros, World Scientific Publ. Comp., Singapore, 1994, 821 pp. | MR | Zbl

[7] Fischer B., “Chebyshev polynomials for disjoint compact sets”, Constr. Approx., 8:3 (1992), 309–329 | DOI | MR | Zbl

[8] Peherstorfer F., “Minimal polynomials for the compact sets of the complex plane”, Constr. Approx., 12:4 (1996), 481–488 | DOI | MR | Zbl

[9] Borodin P.A., “Ob odnom uslovii na mnogochlen, dostatochnom dlya minimalnosti ego normy na zadannom kompakte”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2006, no. 4, 14–18 | Zbl

[10] Pestovskaya A.E., “Mnogochleny, naimenee uklonyayuschiesya ot nulya, s ogranicheniem na raspolozhenie kornei”, Tr. In-ta matematiki i mekhaniki UrO RAN, 28:3 (2022), 166–175 | DOI | MR

[11] Suetin P.K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1979, 416 pp.

[12] Kochurov A.S., Tikhomirov V.M., “Ob ekstrapolyatsii polinomov s deistvitelnymi koeffitsientami v kompleksnuyu ploskost”, Mat. zametki, 106:4 (2019), 543–548 | DOI | MR | Zbl

[13] Shabat B.V., Vvedenie v kompleksnyi analiz. Ch.1. Funktsii odnogo peremennogo, Lan, SPb, 2004, 336 pp. | MR

[14] Goluzin G.M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka GITTL, M.; L., 1952, 628 pp. | MR

[15] Akopyan R.R., “Optimalnoe vosstanovlenie analiticheskoi funktsii po zadannym s pogreshnostyu granichnym znacheniyam”, Mat. zametki, 99:2 (2016), 163–170 | DOI | MR | Zbl