Extremal polynomials related to Zolotarev polynomials
- Авторлар: Agafonova I.1, Malozemov V.1
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Мекемелер:
- St. Petersburg State University
- Шығарылым: Том 93, № 2 (2016)
- Беттер: 164-165
- Бөлім: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223480
- DOI: https://doi.org/10.1134/S1064562416020113
- ID: 223480
Дәйексөз келтіру
Аннотация
Algebraic polynomials bounded in absolute value by M > 0 in the interval [–1, 1] and taking a fixed value A at a > 1 are considered. The extremal problem of finding such a polynomial taking a maximum possible value at a given point b < −1 is solved. The existence and uniqueness of an extremal polynomial and its independence of the point b < −1 are proved. A characteristic property of the extremal polynomial is determined, which is the presence of an n-point alternance formed by means of active constraints. The dependence of the alternance pattern, the objective function, and the leading coefficient on the parameter A is investigated. A correspondence between the extremal polynomials in the problem under consideration and the Zolotarev polynomials is established.
Негізгі сөздер
Авторлар туралы
I. Agafonova
St. Petersburg State University
Хат алмасуға жауапты Автор.
Email: ivagafonovaspb@gmail.com
Ресей, Universitetskaya nab. 7/9, St. Petersburg, 199034
V. Malozemov
St. Petersburg State University
Email: ivagafonovaspb@gmail.com
Ресей, Universitetskaya nab. 7/9, St. Petersburg, 199034