Мақаланы E-mail арқылы жіберу FINITE DECIMAL FRACTIONS AS ENTRIES OF NONSINGULAR MATRICES
- Авторлар: Abramov S.A.1, Ryabenko A.A.1
-
Мекемелер:
- Federal Research Center “Computer Science and Control”, Russian Academy of Sciences
- Шығарылым: № 2 (2025)
- Беттер: 83-90
- Бөлім: COMPUTER ALGEBRA
- URL: https://ogarev-online.ru/0132-3474/article/view/292086
- DOI: https://doi.org/10.31857/S0132347425020104
- EDN: https://elibrary.ru/DIOZTB
- ID: 292086
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
How can one check, for a given nonsingular real number matrix the entries of which have only a finite number of decimal digits, whether this matrix will remain nonsingular after some decimal digits are arbitrarily added to some (explicitly specified in advance) of its entries? It turns out that this problem is algorithmically solvable. A computer implementation of the proposed algorithmic solution is discussed.
Авторлар туралы
S. Abramov
Federal Research Center “Computer Science and Control”, Russian Academy of Sciences
Email: sergeyabramov@mail.ru
Moscow, Russia
A. Ryabenko
Federal Research Center “Computer Science and Control”, Russian Academy of Sciences
Email: anna.ryabenko@gmail.com
Moscow, Russia
Әдебиет тізімі
- Abramov S., Barkatou M. On Strongly Non-Singular Polynomial Matrices// In: Schneider C., Zima E. (eds.). Advances in Computer Algebra. Springer Proceedings in Mathematics & Statistics. 2018. Vol. 226. P. 1–17.
- Tarski A. A decision method for elementary algebra and geometry // Santa Monica CA: RAND Corp., 1948.
- Матиясевич Ю.В. АлгоритмТарского // Компьютерные инструменты в образовании. 2008. № 6. С. 4–14.
- Matiyasevich Yu.V. Tarski’s algorithm // Komput. Instrum. v Obrazovanii., 2008, no. 6, pp. 4–14.
- Collins G.E. Quantifier elimination for real closed fields by cylindrical algebraic decomposition // In Proc. 2nd GI Conf. Automata Theory and Formal Languages. New York: Springer-Verlag, 1975. P. 134–183.
- Davenport J., Heintz J. Real quantifier elimination is doubly exponential // J. Symb. Comput. 1988.№5. P. 29–35.
- Дэвенпорт Дж., Сирэ И., Турнье Э. Компьютерная алгебра. Системы и алгоритмы алгебраических вычислений. М.: Мир, 1991.
- Davenport J., Siret Y., Tournier E. Calcul formel, Paris: Masson, 1987.
- Абрамов С.А., Рябенко А.А. О строго невырожденных числовых матрицах // Труды XV научной конференции “Дифференциальные уравнения и смежные вопросы математики”. Коломна: ГСГУ, 2025. С. 19–24.
- Abramov S.A., Ryabenko A.A.Onstrongly nonsingular number matrices // Trudy XV Nauchn. Konf. On Differential Equations and Related Problems of Mathematics, Kolomna: Gos. Sotsial’noGumanitarnyi Univ. 2025. P. 19–24.
- Basu S., Pollack R., Coste-Roy M.-F. Algorithms in real algebraic geometry // Algorithms and Computation in Mathematics. Vol. 10. Springer, 2006.
- Caviness B.F., Johnson J.R. (eds.). Quantifier elimination and cylindrical algebraic decomposition // Texts & Monographs in Symbolic Computation, Springer, 1998.
- Maple online help: http://www.maplesoft.com/support/help/
- Tonks Z. A Poly-algorithmic quantifier elimination package in Maple // In Jurgen Gerhard and Ilias Kotsireas, editors, Maple in Mathematics Education and Research. Springer International Publishing. 2020. P. 176–186.
- http://www.ccas.ru/ca/_media/str_nonsing.mw
- http://www.ccas.ru/ca/_media/str_nonsing.pdf
- Кострикин А.И. Введение в алгебру. М.: Физматлит, 1977.
- Kostrikin A.I. Introduction to Algebra, Berlin: Springer, 1982.
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