Polynomial interpolation problem for skew polynomials
Апстракт
Let R = K[x;δ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based on properties of skew polynomial rings, and it makes possible some useful theorems about them. The main result of this paper is a generalization of polynomial interpolation problem for skew polynomials. We present conditions under which there exists a unique polynomial of a degree less then n which takes prescribed values at given points xi Є K (1 ≤ n). We also discuss some kind of Silvester-Lagrange skew polynomial.
Кључне речи:
interpolation / skew polynomialsИзвор:
Applicable Analysis and Discrete Mathematics, 2007, 1, 2, 403-414Издавач:
- Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
DOI: 10.2298/AADM0702403E
ISSN: 1452-8630
WoS: 000207680700009
Scopus: 2-s2.0-78650939388
Колекције
Институција/група
GraFarTY - JOUR AU - Erić, Aleksandra PY - 2007 UR - https://grafar.grf.bg.ac.rs/handle/123456789/161 AB - Let R = K[x;δ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based on properties of skew polynomial rings, and it makes possible some useful theorems about them. The main result of this paper is a generalization of polynomial interpolation problem for skew polynomials. We present conditions under which there exists a unique polynomial of a degree less then n which takes prescribed values at given points xi Є K (1 ≤ n). We also discuss some kind of Silvester-Lagrange skew polynomial. PB - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd T2 - Applicable Analysis and Discrete Mathematics T1 - Polynomial interpolation problem for skew polynomials EP - 414 IS - 2 SP - 403 VL - 1 DO - 10.2298/AADM0702403E ER -
@article{ author = "Erić, Aleksandra", year = "2007", abstract = "Let R = K[x;δ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based on properties of skew polynomial rings, and it makes possible some useful theorems about them. The main result of this paper is a generalization of polynomial interpolation problem for skew polynomials. We present conditions under which there exists a unique polynomial of a degree less then n which takes prescribed values at given points xi Є K (1 ≤ n). We also discuss some kind of Silvester-Lagrange skew polynomial.", publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd", journal = "Applicable Analysis and Discrete Mathematics", title = "Polynomial interpolation problem for skew polynomials", pages = "414-403", number = "2", volume = "1", doi = "10.2298/AADM0702403E" }
Erić, A.. (2007). Polynomial interpolation problem for skew polynomials. in Applicable Analysis and Discrete Mathematics Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 1(2), 403-414. https://doi.org/10.2298/AADM0702403E
Erić A. Polynomial interpolation problem for skew polynomials. in Applicable Analysis and Discrete Mathematics. 2007;1(2):403-414. doi:10.2298/AADM0702403E .
Erić, Aleksandra, "Polynomial interpolation problem for skew polynomials" in Applicable Analysis and Discrete Mathematics, 1, no. 2 (2007):403-414, https://doi.org/10.2298/AADM0702403E . .