On Bilinear Complexity of Multiplying 2 × 2-Matrix by 2 × m-Matrix over Finite Field
- Авторлар: Alekseev V.B.1, Nazarov A.A.1
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Мекемелер:
- Department of Computational Mathematics and Cybernetics
- Шығарылым: Том 43, № 4 (2019)
- Беттер: 149-155
- Бөлім: Article
- URL: https://journals.rcsi.science/0278-6419/article/view/176320
- DOI: https://doi.org/10.3103/S0278641919040022
- ID: 176320
Дәйексөз келтіру
Аннотация
The problem of the least number of multiplications required to compute the product of a 2 × 2-matrix X and a 2 × m-matrix Y over an arbitrary finite field is considered by assuming that the elements of the matrices are independent variables. No commutativity of elements of matrix X with elements of matrix Y is assumed (i.e., bilinear complexity is considered). Upper bound \(\frac{{7m}}{2}\) for this problem over an arbitrary field is known. For two-element field, this bound is exact. Lower bound (3 + \(\frac{3}{{{K^2} + 2}}\)) m is obtained for the least number of multiplications in this problem over an arbitrary finite field with K elements.
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Авторлар туралы
V. Alekseev
Department of Computational Mathematics and Cybernetics
Хат алмасуға жауапты Автор.
Email: vbalekseev@rambler.ru
Ресей, Moscow, 119991
A. Nazarov
Department of Computational Mathematics and Cybernetics
Хат алмасуға жауапты Автор.
Email: nazarovandry2@mail.ru
Ресей, Moscow, 119991
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